Research on Weighted Logical Inference for Uncertain Fault Diagnosis
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摘要: 针对复杂系统故障诊断建模及推理的复杂性、数据不足、领域知识及监测信息不完备等问题, 本文基于动态不确定因果图(Dynamic uncertain causality graph, DUCG)进行权重逻辑推理(Weighted logical inference, WLI)及其数理基础的系统化研究. WLI引入绑定权重系数的逻辑事件推理机制, 可确保变量状态概率的自动归一性和链式推理的自我依赖性, 为多赋值因果关系的简洁、不完备表达提供了解决方案. 由于WLI在信息不完全性和命题真值空间的高维性等方面突破了经典数理逻辑, 为使其理论基础更为坚实, 本文进行了WLI的规范化定义、推理算法补充、运算性质探析, 并就理论相容性和自洽性开展了详细论证. 算法分析及故障诊断实验结果表明, 其高效、准确、较少依赖于参数精确性和数据完备性等特征.Abstract: To solve the problems of fault diagnosis of complex systems such as modeling complexity, computational overload, insufficient data, and incomplete knowledge and observations, this paper systematically investigates the algorithm and its mathematical foundation for weighted logical inference (WLI) by means of dynamic uncertain causality graph (DUCG). After introducing a novel mechanism of logic event inference that is accompanied by algebraic operation of weighting factor, WLI is characterized as "self-relied" chaining inference which guarantees the auto-normalization of variables' state probabilities, providing solutions for compact and incomplete representation of multi-valued causalities. Since WLI is beyond the realm of classical mathematical logic in respects of incomplete information and high dimension of propositional truth value space, this paper presents its formal definitions, supplements the inference algorithms, and analyzes the operational features in order to ensure the theoretical rigorousness. Also, the theoretic self-containment and self-consistency are proven in detail. The results of algorithm analysis and fault diagnosis experiments indicate WLI's efficiency, accuracy, and less dependency on the preciseness of parameters and completeness of observations.
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