A non-parametric indicator Kriging method for generating coastal sediment type map

Coastal sediment type map has been widely used in marine economic and engineering activities, but the traditional mapping methods had some limitations due to their intrinsic assumption or subjectivity. In this paper, a non-parametric indicator Kriging method has been proposed for generating coastal sediment map. The method can effectively avoid mapping subjectivity, has no special requirements for the sample data to meet second-order stationary or normal distribution, and can also provide useful information on the quantitative evaluation of mapping uncertainty. The application of the method in the southern sea area of Lianyungang showed that much more convincing mapping results could be obtained compared with the traditional methods such as IDW, Kriging and Voronoi diagram under the same condition, so the proposed method was applicable with great utilization value.

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.

Entropy method for determination of weight of evaluating indicators in fuzzy synthetic evaluation for water quality assessment

Considering the difficulty of fuzzy synthetic evaluation method in calculation of the multiple factors and ignorance of the relationship among evaluating objects, a new weight evaluation process using entropy method was introduced. This improved method for determination of weight of the evaluating indicators was applied in water quality assessment of the Three Gorges reservoir area. The results showed that this method was favorable for fuzzy synthetic evaluation when there were more than one evaluating objects. One calculation was enough for calculating every monitoring point. Compared with the original evaluation method, the method predigested the fuzzy synthetic evaluation process greatly and the evaluation results are more reasonable.

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 meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation

Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging inter- polation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail.

Evaluation Indicators and Extraction Method for Pitting Corrosion of Structural Steel

A set of evaluation indicators based on corrosion ratio in theory for assessing the extent of pitting corrosion and performance reduction are proposed. In order to quantify the morphology of pitting corrosion and extract the evaluation indicators,the 3D profile data obtained by pitting morphology measurement are imported into a special written program to automatically determine the location of each corrosion pit and distill any desired data pertinent to the pitting morphology. The results show that this method seems to be effective to analyze the corroded surface and characterize the pitting morphology.

基于Kriging模型与FORM的钢板组合梁桥结构优化设计

考虑材料参数的不确定性以及设计变量多重约束条件的影响,提出了基于可靠性分析的钢板组合梁桥结构优化设计方法。首先,利用拉丁超立方试验设计(Latin hypercube design,LHD)构建试验组合方案,并通过有限元分析获取试验设计组合下的最大挠度响应值。基于获取的训练样本,构建能够表征结构最大挠度值与随机输入之间映射关系的Kriging代理模型。基于建立的代理模型,以钢结构截面积最小化为目标函数,建立符合规范要求与可靠度约束的优化数学模型,并采用一阶可靠性方法(first order reliability method,FORM),实现设计变量优化。通过比较具有相同设计变量上限,但下限分别为初始值的80%和70%两种优化设计方案,评估了两者在相同阈值以及不同阈值下设计变量的优化结果。最后对方案二在阈值为17 mm下的优化结果进行极限状态验算。结果表明:两个优化设计方案在阈值为17 mm下的优化结果更具合理性,并且方案二在同一阈值下具有更高的优化程度。随着阈值增加,优化程度增加,且腹板高度在较大阈值下对结果影响更大,而翼缘宽度在较小阈值下影响更大。

Optimization of Sensor Orientation in Railway Wheel Detector, Using Kriging Method

Considering the importance of axle counter function in detecting the train wheels and determining the clearance or occupancy of a track section, it is important to ensure a safe and reliable performance of this system. In this paper, in order to improve the sensor performance, the authors have focused on the orientation of magnetic sensors’ coils. In order to improve the detection capability of the system, through measuring the induced voltage in the receiver coil, it is important to adjust the relative orientation of the transmitter and receiver coils. Due to the existence of infinite relative orientations, in order to determine the optimum orientation for the sensor coils, Kriging methods which is one of the Response Surface Methodologies (RSMs) is applied. Finite Element Method (FEM) is utilized to provide sample data, as inputs to the Kriging algorithm. The analysis not only provides the optimum relative orientation of the sensor coils, it also improves analysis time, comparing to field based measurements. The analysis results are validated by the laboratory based data implemented in the control and signaling laboratory of the school of railway engineering and also field based tests in Iranian railway.

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.

Optimization of buckling load for laminated composite plates using adaptive Kriging-improved PSO:A novel hybrid intelligent method

An effective hybrid optimization method is proposed by integrating an adaptive Kriging(A-Kriging)into an improved partial swarm optimization algorithm(IPSO)to give a so-called A-Kriging-IPSO for maximizing the buckling load of laminated composite plates(LCPs)under uniaxial and biaxial compressions.In this method,a novel iterative adaptive Kriging model,which is structured using two training sample sets as active and adaptive points,is utilized to directly predict the buckling load of the LCPs and to improve the efficiency of the optimization process.The active points are selected from the initial data set while the adaptive points are generated using the radial random-based convex samples.The cell-based smoothed discrete shear gap method(CS-DSG3)is employed to analyze the buckling behavior of the LCPs to provide the response of adaptive and input data sets.The buckling load of the LCPs is maximized by utilizing the IPSO algorithm.To demonstrate the efficiency and accuracy of the proposed methodology,the LCPs with different layers(2,3,4,and 10 layers),boundary conditions,aspect ratios and load patterns(biaxial and uniaxial loads)are investigated.The results obtained by proposed method are in good agreement with the literature results,but with less computational burden.By applying adaptive radial Kriging model,the accurate optimal resultsebased predictions of the buckling load are obtained for the studied LCPs.

Risk reduction in Sechahun iron ore deposit by geological boundary modification using multiple indicator Kriging

Uncertainty on the geological contacts and the block volumes of the models along boundaries is often a major part of the global uncertainty of reserve estimation.This work introduces a geostatistical technique that has been developed and tested in an iron ore deposit at Bafq mining district,in central Iran,and that,based on a probability criterion,helps to objectively model the geometry of this iron ore deposit.The main problem in reserve estimation of this ore body is its geometrical modeling and uncertainty in geological boundaries.This work deals with the geostatistical method of multiple indicator kriging,which is used to determine the real boundaries of ore body in different categories.This approach has potential to improve project performance and decrease operational risk.For this purpose,the ore body is separated into two categories including rich iron zone(w(Fe)>45%)and poor iron zone(20%<w(Fe)<45%).It significantly benefits to decrease the risk of reserve evaluation in the deposit.This case study also highlights the value of multiple indicator kriging as a tool for estimates the position of grade boundaries within the deposit.Comparison of the resultant probability maps with the real ore/waste contacts on the extracted levels shows that the first indicator model could separate the whole ore body(poor plus rich)from the waste zone by probability of more than 0.35,which concludes the total reserve of 53 million tons.The second indicator model applied to separate the rich and poor domains and the results show that the blocks with the estimated probability of equal to or more than 0.4 lay within the rich ore zone consisting of 15.8 million tons reserve.

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.

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.

Identification of Sustainability Indicators and Evaluation of Transportation Corridors during Construction Using Fuzzy VIKOR Method

Sustainability is popularly defined as meeting the needs of the present generation without compromising the ability of future generations to meet their own needs. Social, economic and environmental parameters are most commonly accepted as the three pillars of sustainability. In this paper, various sustainability indicators have been identified during the construction stage for elevated transportation corridors and thereafter classified under various categories. Using fuzzy VIKOR technique, sustainability evaluation of transportation corridors is made on two selected project sites of two different government organizations using various identified sustainability indicators, i.e., a 3.2-km long elevated road project under construction from Vikaspuri to Meerabagh in West Delhi by PWD （Public Works Department） and the metro rail elevated corridor （part） from Punjabi Bagh to Mayapuri as a part of Phase 3, Line 7 by DMRC （Delhi Metro Rail Corporation）. The study is made at both sites in the midst of the construction period and it is identified that during the construction stage, the sustainability of these transportation corridors is just not limited to three pillars, but in actuality, it is much beyond that. From the study, it is inferred that the metro rail elevated corridor is a more sustainable corridor, in the context of the identified sustainability indicators.

基于自适应多保真度Co-Kriging代理模型的地下水污染源反演识别

为高效率高精度地进行地下水污染源反演识别,综合运用高保真度和低保真度地下水溶质运移数值模拟模型,研究应用集成差分进化算法的Co-Kriging方法建立模拟模型的多保真度代理模型;在此基础上,探索应用马尔科夫链蒙特卡洛(MCMC)-DREAM_((D))算法,并采用自适应更新多保真度代理模型策略进行地下水污染源反演识别.为验证上述方法的有效性和可行性,开展了数值算例研究.结果表明:相比仅基于高保真度模型输入-输出样本构建的Kriging代理模型,联合运用高保真度和低保真度模型输入-输出样本构建的Co-Kriging代理模型对模拟模型的逼近精度更高;耦合多保真度Co-Kriging代理模型和MCMC-DREAM_((D))算法能够得到较高精度的污染源反演结果,且能够大幅度减小计算负荷;同时,采用自适应更新多保真度代理模型策略能够进一步提高污染源反演识别精度.

Impacts of Aggregation Methods and Trophospecies Number on the Structure and Function of Marine Food Webs

Aggregation of species with similar ecological properties is one of the effective methods to simplify food web researches.However,species aggregation will affect not only the complexity of modeling process but also the accuracy of models’outputs.Selection of aggregation methods and the number of trophospecies are the keys to study the simplification of food web.In this study,three aggregation methods,including taxonomic aggregation(TA),structural equivalence aggregation(SEA),and self-organizing maps(SOM),were analyzed and compared with the linear inverse model–Markov Chain Monte Carlo(LIM-MCMC)model.Impacts of aggregation methods and trophospecies number on food webs were evaluated based on the robustness and unitless of ecological net-work indices.Results showed that aggregation method of SEA performed better than the other two methods in estimating food web structure and function indices.The effects of aggregation methods were driven by the differences in species aggregation principles,which will alter food web structure and function through the redistribution of energy flow.According to the results of mean absolute percentage error(MAPE)which can be applied to evaluate the accuracy of the model,we found that MAPE in food web indices will increase with the reducing trophospecies number,and MAPE in food web function indices were smaller and more stable than those in food web structure indices.Therefore,trade-off between simplifying food webs and reflecting the status of ecosystem should be con-sidered in food web studies.These findings highlight the importance of aggregation methods and trophospecies number in the analy-sis of food web simplification.This study provided a framework to explore the extent to which food web models are affected by dif-ferent species aggregation,and will provide scientific basis for the construction of food webs.

基于LHS-Kriging-DW的页岩气集输管道内腐蚀预测模型研究

为了准确预测页岩气集输管道的内腐蚀速率,对DW(DeWarrd)模型进行修正,运用LHS(拉丁超立方抽样)优化的Kriging(克里金方法)对修正DW进行训练以建立模型并验证。通过高清漏磁检测器检测某页岩气集输管道内腐蚀速率,基于PIPESIM模拟该管道现场工况,运用多元非线性回归修正DW模型。运用LHS-Kriging对修正DW模型进行训练并优化,运用建立的模型对另一相邻管道进行了腐蚀速率的预测和现场开挖验证。现场内检测的结果显示:管线在几处低洼积液处发生了严重的腐蚀,因此引入了持液率作为修正因子修正DW模型。选择样本数为500用于LHS-Kriging-DW模型时误差较小。在实例运用中,10个开挖检测点有9个都在预测结果的95%置信区间内,这说明建立的腐蚀速率模型可用于指导现场内腐蚀直接评价等相关工作。

Comprehensive Evaluation of Distributed PV Grid-Connected Based on Combined Weighting Weights and TOPSIS-RSR Method

To effectively quantify the impact of distributed photovoltaic(PV)access on the distribution network,this paper proposes a comprehensive evaluation method of distributed PV grid connection combining subjective and objective combination of assignment and technique for order preference by similarity to an ideal solution(TOPSIS)—rank sum ratio(RSR)(TOPSIS-RSR)method.Based on the traditional distribution network evaluation system,a comprehensive evaluation system has been constructed.It fully considers the new development requirements of distributed PV access on the environmental friendliness and absorptive capacity of the distribution grid and comprehensively reflects the impact of distributed PV grid connection.The analytic hierarchy process(AHP)was used to determine the subjective weights of the primary indicators,and the Spearman consistency test was combined to determine the weights of the secondary indicators based on three objective assignment methods.The subjective and objective combination weights of each assessment indicator were calculated through the principle of minimum entropy.Calculate the distance between the indicators to be evaluated and the positive and negative ideal solutions,the relative closeness ranking,and qualitative binning by TOPSIS-RSR method to obtain the comprehensive evaluation results of different scenarios.By setting up different PV grid-connected scenarios and utilizing the IEEE33 node simulation algorithm,the correctness and effectiveness of the proposed subject-object combination assignment and integrated assessment method are verified.

Application of NSR-AISC Method in Reserve Estimation and Technical Economic Evaluation of Low-Grade Polymetallic Deposits: Taking a Low-Grade Copper-Molybdenum Mine in Guangdong Province as an Example

The development and utilization of low-grade polymetallic deposits with strategic mineral resources is one of the important measures to alleviate the current high dependence on strategic mineral resources in China. However, domestic mining enterprises and most mining consulting and design institutes usually use general industrial indicators to carry out reserve estimation and technical and economic feasibility studies on low-grade polymetallic deposits, which cannot truly reflect the economic value of such deposits. The article expounds on the definitions of net return value (NSR) and on-site total maintenance cost (AISC) of common ore smelters in the evaluation of overseas mineral resources. Taking a low-grade polymetallic copper-molybdenum mine in Guangdong Province as an example, comparing the research results showed the NSR-AISC method and the general industrial index method in low-grade polymetallic deposit. There are huge differences in the results of reserve estimation;through the further introduction of Taylor’s formula and the research results on the relationship between investment intensity and production scale, a more reasonable mine life and investment scale are recommended, and a more in-depth comparative study has been carried out in the dimension of technical and economic indicators. Based on the comparative study of the above two methods in reserve estimation and the evaluation results of technical and economic indicators, the author believes that the NSR-AISC method can better reflect the true value of low-grade polymetallic ore projects, and should be popularized and applied in resource evaluation and development practice. This article further describes the application status of the NSR-AISC method for reserve estimation and the evaluation of technical economic indicators, and suggests the main points that should be paid attention to in the use of the NSR-AISC method.

Kriging与Breitung融合的可靠性分析方法

针对一阶可靠性方法在处理非线性极限状态函数时精度不足,以及Breitung方法在随机变量维度较高时计算效率低的问题,提出融合Kriging模型与Breitung方法的可靠性分析策略。采用一阶可靠性方法求解极限状态函数的最大可能失效点,并基于迭代过程中产生的样本点训练Kriging模型。通过Breitung方法计算Kriging模型在最大可能失效点各方向上的曲率,并据此构建近似抛物面。为避免Breitung方法概率公式中的奇异解问题,引入鞍点近似来计算近似抛物面的失效概率。通过3个数值算例和一个复合材料压力容器的工程实例对比一阶可靠性方法、Breitung方法以及融合Kriging与Breitung的可靠性分析方法的效率与精度。结果显示,融合Kriging与Breitung的可靠性分析方法不仅提高了计算效率,并且求解过程稳定,具有较高的求解精度。