Abstract: Current research on belief rule base (BRB) focuses on single BRB system, however, the reasoning performance of single BRB system is influenced by the values of parameters. And the uneven distribution or small amount of training data can lead to the incompleteness of training parameters, which makes the locality of information for decision provided by reasoning results. To solve these problems, this paper proposes BRB-ensemble system base in gradient descent algorithm (GDA) via combining the Bagging and AdaBoost with BRB respectively, and the BRB system is applied to the pipeline leak detection and multimodal function fitting. The performance of BRB system can be improved by the integration of multiple sub-BRB. In the case study, the convergence accuracy and fitting effect are used to analyze the performance of BRB-ensemble, and the proposed approach is compared with other single BRB system. The experimental results show that the BRB-ensemble method is reasonable and effective.

Key words: belief rule base (BRB), ensemble learning, gradient descent algorithm (GDA), Bagging, AdaBoost

摘要： 目前对置信规则库（belief rule base，BRB）的研究主要针对单个BRB系统，然而单个BRB系统的推理性能不仅受参数取值的影响，而且当训练集分布不均衡或数据量较少时，容易导致参数训练不全面，从而使得推理结果所提供的决策信息存在局部性。通过引入Bagging算法和AdaBoost算法，分别与BRB相结合提出了基于梯度下降法（gradient descent algorithm，GDA）的置信规则库系统的集成学习方法，并分别应用于输油管道检漏、多峰函数的置信规则库训练，将多个BRB子系统集成，提高系统的推理性能。在实验中，以收敛精度和曲线拟合效果作为衡量指标来分析集成系统的性能，并将集成系统与其他单个BRB系统进行比较，实验结果表明BRB集成学习方法合理有效。

关键词: 置信规则库（BRB）, 集成学习, 梯度下降法（GDA）, Bagging, AdaBoost