Fault Tree Ring Closure Normalization for Minimal Cutset Analysis
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Solution Overview
Problem
Existing fault tree analysis methods struggle with handling ring closures, which can lead to undetermined minimal cutsets and complicate safety assurance in safety-critical systems due to the inability of Boolean logic to handle loops.
Innovation Solution
A method involving the replacement of ring closures in fault trees with predefined expressions, such as variables, to create a placeholder fault tree that can be normalized, allowing for efficient analysis and safety assurance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If fault tree analysis is performed on systems with ring closures using Boolean logic, then the analysis can be performed with standard methods, but the minimal cutsets cannot be determined and the analysis becomes invalid
Solution Approach 1:
The fault tree is segmented by identifying and isolating ring closure structures. The method breaks down the complex fault tree with loops into manageable components by detecting ring closures and applying specific normalization rules to these segments, allowing standard Boolean analysis to be applied to the remaining acyclic portions.
Solution Approach 2:
The method changes the structural parameters of the fault tree by applying normalization rules that transform the representation of ring closures. This involves modifying how cyclic dependencies are expressed in the Boolean logic, converting them into equivalent acyclic representations that preserve the original system's failure logic while eliminating the loop structure.
2Productivity
If ring closures are detected and handled by replacement with variables, then the fault tree can be normalized and analyzed, but the complexity of the analysis process increases
Solution Approach 1:
The method performs preliminary detection of ring closures before executing the main fault tree analysis. By identifying cyclic structures in advance and preparing their normalized representations, the method prevents analysis failures and reduces computational complexity during the actual minimal cutset calculation phase.
Solution Approach 2:
The method introduces intermediate variables to represent ring closure structures during normalization. These intermediary elements serve as placeholders that capture the cyclic dependency relationships, allowing the fault tree to be transformed into an equivalent acyclic form that can be processed by standard Boolean analysis tools.
3Ease of operation
If standard Boolean logic is used for fault propagation modeling, then the logic is simple and well-understood, but loops cannot be contained and ring closures cannot be handled
Solution Approach 1:
Instead of trying to make Boolean logic handle loops directly, the method inverts the approach by transforming the fault tree structure to eliminate loops. It converts cyclic dependencies into equivalent acyclic representations, allowing standard Boolean logic to remain unchanged while gaining the ability to handle systems with feedback loops and ring closures.
Data Source
AI summary
One or more ring closures of a fault tree are provided. For each one of the one or more ring closures: at least one respective edge the respective ring closure is replaced in the fault tree by a respective variable to obtain a placeholder fault tree and a normalized representation of the placeholder fault tree is determined.