岩体质量评价的分形插值模型
来源期刊：中南大学学报(自然科学版)2012年第12期
论文作者：王威 苏经宇 马东辉 田杰
文章页码：4827 - 4833
关键词：分形插值模型；分维数；岩体质量；评价
Key words：fractal interpolation model; fractal dimension; rock mass quality; evaluation
摘 要：岩体质量分类是一个复杂的不确定系统问题，为准确评价岩体质量所处的分类状态，进而为岩体质量的防治提供科学依据，提出基于分形-插值模型的岩体质量评价方法。该方法首先选取影响岩体质量评价的8个主要因素，根据分类标准，采用在每级标准中随机内插的方法，得到50个标准样本，用于构建岩体质量评价的分形-插值模型；其次，根据最大似然分类原则确定每个岩体质量评价指标的评价分维数；然后，利用加权求和法计算样本的综合评价值，并根据样本综合评价值与经验等级之间的关系建立分形-插值评价模型；最后，通过实例分析表明：该模型的评价结果是准确和可靠的，与采用其他分类方法所得结论一致。此外，该模型可以得出每个样本的具体得分值，即使对属于同一级的样本也可以排出它们的优劣顺序，因而具有较高的分类精度，为岩体质量评价提供了一种较好的新方法。
Abstract: Evaluation of rock mass quality is a complex system problem with uncertainty. For the sake of accurate evaluation of the estate of rock mass quality, and to provide scientific basis for the prevention of rock mass quality, the evaluating method for rock mass quality based on fractal interpolation theory was brought forward. Firstly, eight key factors were chosen to construct the model. In addition, because of few standard samples, fifty standard samples were produced by the way of stochastic interpolation on basis of classification standard. Secondly, through calculating the fractal dimension of single index of rock mass quality, the fractal dimension exponent evaluation of the index of single rock mass quality with the maximum likelihood classification principle was confirmed. Thirdly, adopting weighted summation value this method calculated the level of the colligate estimation of multi-index of rock mass quality and established the fractal interpolation evaluation model according to the relationship between the value of comprehensive evaluation of the samples and the experience level. Finally, four samples were classified based on the model. The classification results are consistent with that from other methods. It is shown that the model here is feasible and effective in evaluating rock mass quality. Moreover, particular score of each sample can be computed by the model, and so it has more precise classification and is a better new method.
王威1, 2，苏经宇1，马东辉1，田杰2
(1. 北京工业大学 抗震减灾研究所，北京，100124；
2. 北京工业大学 建筑工程学院，北京，100124)
摘 要：岩体质量分类是一个复杂的不确定系统问题，为准确评价岩体质量所处的分类状态，进而为岩体质量的防治提供科学依据，提出基于分形-插值模型的岩体质量评价方法。该方法首先选取影响岩体质量评价的8个主要因素，根据分类标准，采用在每级标准中随机内插的方法，得到50个标准样本，用于构建岩体质量评价的分形-插值模型；其次，根据最大似然分类原则确定每个岩体质量评价指标的评价分维数；然后，利用加权求和法计算样本的综合评价值，并根据样本综合评价值与经验等级之间的关系建立分形-插值评价模型；最后，通过实例分析表明：该模型的评价结果是准确和可靠的，与采用其他分类方法所得结论一致。此外，该模型可以得出每个样本的具体得分值，即使对属于同一级的样本也可以排出它们的优劣顺序，因而具有较高的分类精度，为岩体质量评价提供了一种较好的新方法。
关键词：分形插值模型；分维数；岩体质量；评价
WANG Wei1, 2, SU Jing-yu1, MA Dong-hui1, TIAN Jie2
(1. Institute of Earthquake Resistance and Disaster Reduction, Beijing University of Technology, Beijing 100124, China;
2. College of Civil Engineering, Beijing University of Technology, Beijing 100124, China)
Abstract:Evaluation of rock mass quality is a complex system problem with uncertainty. For the sake of accurate evaluation of the estate of rock mass quality, and to provide scientific basis for the prevention of rock mass quality, the evaluating method for rock mass quality based on fractal interpolation theory was brought forward. Firstly, eight key factors were chosen to construct the model. In addition, because of few standard samples, fifty standard samples were produced by the way of stochastic interpolation on basis of classification standard. Secondly, through calculating the fractal dimension of single index of rock mass quality, the fractal dimension exponent evaluation of the index of single rock mass quality with the maximum likelihood classification principle was confirmed. Thirdly, adopting weighted summation value this method calculated the level of the colligate estimation of multi-index of rock mass quality and established the fractal interpolation evaluation model according to the relationship between the value of comprehensive evaluation of the samples and the experience level. Finally, four samples were classified based on the model. The classification results are consistent with that from other methods. It is shown that the model here is feasible and effective in evaluating rock mass quality. Moreover, particular score of each sample can be computed by the model, and so it has more precise classification and is a better new method.
Key words:fractal interpolation model; fractal dimension; rock mass quality; evaluation
