加权证据权模型和逐步证据权模型及其在个旧锡铜矿产资源预测中的应用

为了消除和减弱当证据层不满足条件独立性假设时对预测结果产生的影响, 提出了逐步证据权模型和加权证据权模型.加权证据权模型通过对logit模型进行修改, 对各个证据层给予一定的权重, 以调整由于证据层与其他证据层的条件相关性对模型的影响; 逐步证据权模型是将证据层按照一定的顺序逐步加入到模型中, 在加入到模型的过程中依次用已经获得的后验概率作为模糊训练层的方法.以个旧锡铜多金属矿产资源预测为例, 应用4种证据权模型的后验概率进行异常圈定, 结果表明两种新的模型对减弱证据层不满足条件独立性假设所产生的影响是有效的.      

增强证据权(BoostWofE)新方法在矿产资源定量评价中的应用

证据权方法是矿产资源定量评价的最常用方法之一,尤其是在GIS环境下,证据权方法具有简便、直观、易实现等优点。然而,证据权模型对证据图层之间满足条件独立性的要求过于苛刻。实际应用中证据图层之间往往不满足条件独立性而导致后验概率计算结果的偏差,这一数学模型上的缺陷严重影响到该方法的使用范围,甚至有时造成预测人员对如何构建证据图层的误解。提出了一种新的增强证据权的模型和计算方法:该模型按顺序加入证据图层,依次计算证据图层的条件权重,并以此累积更新后验概率;新的计算方法可依次对训练点集(预测对象)进行加权处理,并以此为基础逐次计算证据图层的条件权重。介绍了增强证据权理论模型和计算方法,并通过应用实例对比了普通证据权方法和增强证据权方法的应用效果。结果表明:由于增强证据权模型不要求证据图层之间具备条件独立性,它克服了证据权模型的缺陷,显著提高了证据权方法的应用精度,有望扩大证据权方法的应用范围。     

混合模糊证据权模型在河北承德煤炭资源预测中的应用

应用模糊逻辑法、加权证据权法相结合的混合模糊证据权模型和GeoDASGIS技术开展了承德煤炭资源预测研究。采用模糊逻辑法对与煤炭矿床有关的证据层进行了系统的处理和分析,并在此基础上采用加权证据权方法编制了成矿后验概率图,最终划分出5个主要的找矿远景区。研究结果不仅对进一步开展预测区优选评价具有重要的参考意义,而且为混合知识驱动与数据驱动的混合预测模型提供了一种可借鉴的有效方法。     

加权证据权模型的应用与对比

证据权方法是目前最常用的信息综合方法之一,广泛应用于矿产资源定量预测与评价.然而,它要求变量间相互独立,地质上很难满足这一条件.如何削弱条件不独立对证据权预测结果的影响,已成为当前数学地球科学研究的热点.解决该问题的途径之一是对传统证据权模型进行校正,比如采取加权的方法对原证据权模型计算的证据权重进行修正,以便消除非条件独立性的影响.对近期提出的多种加权证据权模型进行了系统的对比研究,基于同样的应用实例和实验方案,对不同方法的应用效果进行了比较,结果表明,各种加权证据权模型均可不同程度地削弱证据图层条件不独立性的影响,其中,基于逻辑回归的加权证据权模型优于其他加权方法.      

基于证据权法的公路路基岩溶塌陷危险性评价

将证据权模型应用在公路路基岩溶发育强度分区中,在工程作用下岩溶强发育区易发生岩溶塌陷。介绍了证据权模型的方法。在丹霞枢纽互通区域,应用Arc GIS将研究区划分为5m×5m的栅格,考虑地层岩性、地下水距地面距离、顶板厚度、距断层距离4个证据因子,然后进行证据因子优选,通过叠加分析,得出岩溶发育强度的后验概率,并进行条件独立性检验,利用CAPP曲线确定阈值将后验概率分区。应用ROC曲线进行预测的精度评价,预测正确概率为66.2%。最后结果表明,证据权模型应用在公路路基岩溶方面可行。     

基于模糊预测对象的证据权方法及其在土地沙漠化评价中的应用

为了使在地理信息系统中被广泛用于点事件预测的证据权方法能对面事件进行评价和预测, 提出了一种新的基于模糊训练层的证据权方法.它是一种更广泛的证据权方法, 与普通证据权方法所不同的是, 它的训练层是模糊集合, 其取值是它的隶属度.通过适当的变换也可以把点训练层转换为模糊集合.因此, 该方法可以对面事件、点事件和线事件进行评价和预测.该方法可以处理训练层和证据层均为模糊集合的情况, 被称为双重模糊证据权方法.作为该方法的一个应用实例, 本文介绍毛乌素沙漠边缘的晋陕蒙地区土地沙漠化评价的应用实例.      

模糊证据权方法在镇沅(老王寨)地区金矿资源评价中的应用

采用模糊证据权方法和GeoDASGIS技术开展了镇沅(老王寨)及其邻区的金矿资源潜力评价.分别采用GeoDASGIS软件提供的局部奇异性分析技术、S-A异常分解技术、主成分分析技术、证据权、模糊证据权等技术对相关地球化学元素进行了系统的处理和分析.应用主成分分析方法确定了可能的2种不同成矿类型,并采用主成分得分确定了组合异常点,在此基础上分别采用普通证据权和模糊证据权方法编制了成矿后验概率图,圈定了有利成矿地段.对比普通证据权方法与模糊证据权方法所得结果表明,模糊证据权方法可减小图层离散化造成的有用信息损失,提高预测结果精度.     

基于GIS证据权重法的陕西旬阳地区铅锌成矿远景区定量预测

针对工作区铅锌矿成因类型利用GIS空间信息系统对地质、物探、化探、遥感等各类异常综合分析与成矿要素的信息提取,并在矿产资源评价分析系统（MORPAS3．0）下建立了陕西旬阳地区铅锌矿证据权重法模型证据图层：赋矿地层、控矿构造、化探异常等18个,通过条件独立性检验确定证据权因子层15个,绘制了陕西旬阳地区铅锌矿资源远景预测区后验概率图,给出了陕西旬阳地区铅锌矿产远景定量预测区评价结论,取得了良好的预测效果。     

ArcGIS证据权模型在铜矿成矿预测中的应用 ——以博格达-哈尔里克成矿带为例

本文选择博格达-哈尔里克一带作为研究区,从区域成矿地质背景入手,鉴于该地区已知成型铜矿床较少,成矿规律研究薄弱,故作者采用ArcGIS平台下的证据权模型(WofE),以数据驱动方式为主,从断裂构造、沉积岩相与建造、火山岩建造、侵入岩岩性等方面,以学生化反差S(C)作为有利因子衡量指标,对各控矿因素进行影响程度分类,利用加权逻辑斯回归模型计算成矿后验概率,根据后验概率值的大小进行成矿远景区的圈定和分级,在博格达-哈尔里克成矿带内共圈定7个成矿远景区。最后结合区域化探资料进行了验证,结果显示所圈定的铜矿成矿远景区内化探异常明显,与Cu元素异常套合较好,说明ArcGIS证据权模型能很好地为区域矿产预测提供良好的技术支撑,为研究区铜矿找矿方向提供理论依据,文中所总结的基于ArcGIS平台的证据权计算方法流程也为区域矿产预测提供了方法借鉴。     

川西北金矿的证据权模型及其预测应用

在深入理解川西北地区金矿成矿特征的 基础上,建立了该区的地质、物探、化探 、遥感和金矿床（点）数据库,优选了10个致矿证据层。应用证据权模型对该区进行成矿分 析,认为本区共有NW、NE、SN、EW四个方向上的金矿成矿区,同时分析了四个成矿区的分布 特征 和空间耦合关系。在此基础上,根据该区成矿概率分布进行了有利成矿远景区的预测,并对 证据权模型在成矿预测中的应用提出了相应的改进意见。     

Application of the content–area (C–A) fractal model and prediction–area (P–A) plot for mineral prospectivity modeling in the Luchun area of Yunnan Province,China

This method of assigning weights based on expert opinion introduces bias when we are evaluating the relative importance of evidence values. In this paper, we used a prediction–area (P–A) plot method and content–area (C–A) fractal model to estimate the weight of each evidence map. In this paper, we used the content region (C–A) fractal model to divide the evidence maps to the threshold of the corresponding dimensions. The P–A plot approach is an objective data-driven approach for evaluating map weights. Using geochemical layer and remote sensing, hydroxyl layers as weight evidence maps are the highlights of this study. We use the P–A method from which we can evaluate the predictive ability of each evidence map with respect to the known ore occurrences. We used the P–A plot for weighting each evidence map and choosing the appropriate threshold for predictor maps in the Luchun area of Yunnan Province, China. The method adopted in this paper can improve the prediction efficiency of ore prospecting.     

A Remark on the Use of a Weight Matrix in the Linear Model of Coregionalization

The linear model of coregionalization (LMC) is generally fit to multivariate geostatistical data by minimizing a least-squares criterion. It is commonly believed that weighting the criterion by inverse variances will reduce the influence of those variables with large variance. We point out that this need not be so, and that in some cases the weights will have no effect whatsoever on the estimated sill matrices. When there is an effect, it is due not to a reduction of these variables’ influence, but rather due to a lack of invariance of the minimization problem; moreover, sometimes the influence may actually increase. The correct way to reduce influence is to fit the LMC after standardizing the variables to have unit variance.     

Omnibus Weights of Evidence Method Implemented in GeoDAS GIS for Information Extraction and Integration

Weights of evidence (WofE) is an artificial intelligent method for integration of information from diverse sources for predictive purpose in supporting decision making. This method has been commonly used to predict point events by integrating point training layer and binary or ternary evidential layers (multiclass evidence less commonly used). Omnibus weights of evidence integrates fuzzy training layer and diverse evidential layers. This method provides new features in comparison with the ordinary WofE method. This new method has been implemented in a geographic information system-geophysical data analysis system and the method includes the following contents: (1) dual fuzzy weights of evidence (DFWofE), in which training layer and evidential layers can be treated as fuzzy sets. DFWofE can be used to predict not only point events but also area or line events. In this model a fuzzy training layer can be defined based on point, line, and areas using fuzzy membership function; and (2) degree-of-exploration model for WofE is implemented through building a degree of exploration map. This method can be used to assess possible spatial correlations between the degree of exploration and potential evidential layers. Importantly, it would also make it possible to estimate undiscovered resources, if the degree of exploration map is combined with other models that predict where such resources are most likely to occur. These methods and relevant systems were validated using a case study of mineral potential prediction in Gejiu (个旧) mineral district, Yunnan (云南), China.     

最优组合赋权法在滑坡综合治理方案决策中的应用

选取安全可靠性、环境协调性、经济合理性、技术可行性、施工难易及施工工期作为评价指标,采用组合赋权法,建立求解主观赋权法(AHP)和客观赋权法(熵权法)的最优组合权重系数的数学规划模型,运用MATLAB求解模型,可得出综合评价值进而决策治理方案。以鲁班崖滑坡综合治理工程实例进行模型运算,结果显示方案2为最佳方案。组合赋权法综合了主观赋权法充分考虑人的主观能动性和客观赋权法反映客观公度的特点,是一种可行、可信和比较符合客观实际的赋权方法。     

A Comparison of Modified Fuzzy Weights of Evidence,Fuzzy Weights of Evidence,and Logistic Regression for Mapping Mineral Prospectivity

Weights of evidence and logistic regression are two of the most popular methods for mapping mineral prospectivity. The logistic regression model always produces unbiased estimates, whether or not the evidence variables are conditionally independent with respect to the target variable, while the weights of evidence model features an easy to explain and implement modeling process. It has been shown that there exists a model combining weights of evidence and logistic regression that has both of these advantages. In this study, three models consisting of modified fuzzy weights of evidence, fuzzy weights of evidence, and logistic regression are compared with each other for mapping mineral prospectivity. The modified fuzzy weights of the evidence model retains the advantages of both the fuzzy weights of the evidence model and the logistic regression model; the advantages being (1) the predicted number of deposits estimated by the modified fuzzy weights of evidence model is nearly equal to that of the logistic regression model, and (2) it can deal with missing data. This method is shown to be an effective tool for mapping iron prospectivity in Fujian Province, China.     

A comparative study of conventional, ANN black box, fuzzy and combined neural and fuzzy weighting procedures for landslide susceptibility zonation in Darjeeling Himalayas

Landslides are one of the most destructive phenomena of nature that cause damage to both property and life every year, and therefore, landslide susceptibility zonation (LSZ) is necessary for planning future developmental activities. In this paper, apart from conventional weighting system, objective weight assignment procedures based on techniques such as artificial neural network (ANN), fuzzy set theory and combined neural and fuzzy set theory have been assessed for preparation of LSZ maps in a part of the Darjeeling Himalayas. Relevant thematic layers pertaining to the causative factors have been generated using remote sensing data, field surveys and Geographic Information System (GIS) tools. In conventional weighting system, weights and ratings to the causative factors and their categories are assigned based on the experience and knowledge of experts about the subject and the study area to prepare the LSZ map (designated here as Map I). In the context of objective weight assignments, initially the ANN as the black box approach has been used to directly produce an LSZ map (Map II). In this approach, however, the weights assigned are hidden to the analyst. Next, the fuzzy set theory has then been implemented to determine the membership values for each category of the thematic layer using the cosine amplitude method (similarity method). These memberships are used as ratings for each category of the thematic layer. Assuming weights of each thematic layer as one (or constant), these ratings of the categories are used for the generation of another LSZ map (Map III). Subsequently, a novel weight assignment procedure based on ANN is implemented to assign the weights to each thematic layer objectively. Finally, weights of each thematic layer are combined with fuzzy set derived ratings to produce another LSZ map (Map IV). The maps I–IV have been evaluated statistically based on field data of existing landslides. Amongst all the procedures, the LSZ map based on combined neural and fuzzy weighting (i.e., Map IV) has been found to be significantly better than others, as in this case only 2.3% of the total area is found to be categorized as very high susceptibility zone and contains 30.1% of the existing landslide area.     

证据权模型中两种预测单元划分方式对比

证据权模型作为一种数据综合方法已被广泛应用于矿产资源定量预测与评价。在模糊证据权基础上,发展了基于地质单元思想的矢量证据图层构建和数据综合方法,并通过实例作具体阐述：它以矿点缓冲区图层作为训练图层,以各证据变量图层在空间上的叠置所形成的唯一地质单元作为评价对象,统一计算各个证据变量的证据权重,进而基于地质单元进行证据综合和后验概率成图。与基于栅格（或规则格网）的模型不同,基于矢量证据权模型以具有明确地质内涵的地质单元（而非规则网格单元）为预测单元,易于解释,并且消除了边界误差;相比基于规则格网划分所得到的成矿单元,以矿床（点）缓冲区作为训练对象,提高了已知矿点的代表性。实例表明：若预测单元大小为初始栅格大小整数倍,各缓冲等级平均面积计算误差为0.26%,否则面积平均误差达到6%;即使在预测单元大小为初始栅格大小整数倍情况下,矿点平均计算误差也达到4.78%。因此,基于地质单元思想的证据权预测单元划分方法在精度上优于基于栅格或规则格网方法。