On the inference and approximation properties of belief rule based systems
On the inference and approximation properties of belief rule based systems
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DOI：
10.1016/j.ins.2013.01.022
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发表时间：
2013-06-10
影响因子：
8.1
通讯作者：
Yang, Shan-Lin
中科院分区：
文献类型：
--
作者：
Chen, Yu-Wang;Yang, Jian-Bo;Yang, Shan-Lin
基于信念规则的推理系统提供了一种通用的推理框架，用于逼近前输入和输出之间复杂的非线性因果关系。它已成功地应用于故障诊断、系统识别和决策分析等广泛领域。本文对BRB系统的推理和近似性质进行了分析和理论分析。首先研究了BRB系统的统一多模型分解结构，在该结构下，输入空间被划分为不同的局部区域。然后分析了BRB系统的分布逼近过程。这些分析结果揭示了使BRB系统具有优越近似性能的潜在推理机制。进一步，利用Stone-Weierstrass定理，构造性地证明了BRB系统可以在紧集合上以任意精度逼近任意连续函数。该结果为BRB系统在实际应用中的使用和训练提供了理论基础。最后，对著名的Box-Jenkins煤气炉基准非线性系统辨识问题进行了数值仿真研究，验证了BRB系统的有效性，并展示了其推理和逼近能力。(C) 2013爱思唯尔公司版权所有。
Belief rule based (BRB) system provides a generic inference framework for approximating complicated nonlinear causal relationships between antecedent inputs and output. It has been successfully applied to a wide range of areas, such as fault diagnosis, system identification and decision analysis. In this paper, we provide analytical and theoretical analyses on the inference and approximation properties of BRB systems. We first investigate the unified multi-model decomposition structure of BRB systems, under which the input space is partitioned into different local regions. Then we analyse the distributed approximation process of BRB systems. These analysis results unveil the underlying inference mechanisms that enable BRB systems to have superior approximation performances. Furthermore, by using the Stone-Weierstrass theorem, we constructively prove that BRB systems can approximate any continuous function on a compact set with arbitrary accuracy. This result provides a theoretical foundation for using and training BRB systems in practical applications. Finally, a numerical simulation study on the well-known benchmark nonlinear system identification problem of Box-Jenkins gas furnace is conducted to illustrate the validity of a BRB system and show its inference and approximation capability. (C) 2013 Elsevier Inc. All rights reserved.