Dynamic Fault Tree Analysis Using Heterogeneous Importance Sampling
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Solution Overview
Problem
Dynamic fault tree analysis, particularly for rare event estimations, is inefficient with existing methods due to the high number of simulations required for accurate results, making it commercially unfeasible for systems like aircraft reliability where failure probabilities are extremely low.
Innovation Solution
The implementation of heterogeneous Importance Samplings characterized by both continuous and discrete Probability Distribution Functions (PDFs), allowing for transitioning between them based on operational parameters, and a stochastic simulator to determine failure probabilities in dynamic fault trees, enabling more efficient and accurate analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing simulation methods are used for dynamic fault tree analysis, then accurate results can be obtained, but the number of simulations required is excessively high making it commercially unfeasible
Solution Approach 1:
The patent changes the parameters of the simulation by using heterogeneous importance sampling with different probability distribution functions (continuous and discrete) to model different phases of system operation. This allows the simulation to focus computational effort on critical failure modes while using fewer total simulations, thereby maintaining accuracy while improving productivity
Solution Approach 2:
The patent introduces dynamic elements by transitioning between continuous and discrete PDFs based on operational parameters such as flight time thresholds. This dynamic adaptation allows the simulation to adjust its sampling strategy during execution, concentrating computational resources on the most relevant failure scenarios and reducing the overall number of simulations needed for accurate results
2Productivity
If heterogeneous Importance Samplings with both continuous and discrete PDFs are used, then the number of simulations needed is reduced, but the complexity of the simulation method increases
Solution Approach 1:
The patent segments the probability distribution into different types (continuous and discrete) that are applied to different portions of the fault tree or different operational phases. This segmentation allows each segment to be handled with the most appropriate sampling method, reducing the total number of simulations needed while managing complexity through modular organization of the sampling strategies
3Productivity
If transitioning between continuous and discrete PDFs is implemented, then simulation efficiency is improved, but the operational complexity of managing different PDF types increases
Solution Approach 1:
The patent implements feedback mechanisms where the simulation monitors operational parameters (such as flight time) and automatically transitions between continuous and discrete PDFs based on predefined thresholds. This feedback-driven approach allows the system to automatically adjust its sampling strategy without requiring manual intervention, improving efficiency while managing operational complexity through automated decision rules
Data Source
AI summary
Disclosed is a dynamic fault tree analysis system including a fault tree module associated with a mission critical system (mcs), wherein said fault tree module includes at least one item characterized by an initial probability density function (pdf), at least one threshold value associated with the mcs, a sampling module to transform the initial pdf to a heterogeneous pdf (hpdf), wherein the hpdf includes at least one continuous segment and at least one discrete segment, and wherein transition between segments is at least partially based on the at least one threshold; and a stochastic simulator to determine the probability of an mcs failure condition by analyzing the fault tree module using the heterogeneous pdf.