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A Graph-based Framework for Complex System Simulating and Diagnosis with Automatic Reconfiguration

Martina Teruzzi, Nicola Demo, Gianluigi Rozza

TL;DR

The paper tackles fault diagnosis and containment in complex industrial systems by modeling plants as weighted directed graphs and introducing a residual service measure to quantify remaining capacity after faults. It combines shortest-path analytics with a fault-propagation model (SINGLE, AND, OR) and employs SWITCH nodes whose states are optimized by genetic algorithms to automatically reconfigure the network and limit cascades. Implemented in SAFEX/GRAPE, the approach yields a practical digital twin capable of simulating faults, diagnosing propagation, and guiding reconfiguration decisions. Results on switch-line and random sparse graphs demonstrate improved residual service and reduced cascade with increased SWITCH deployment, underscoring the framework's potential for plant design, monitoring, and optimization.

Abstract

Fault detection has a long tradition: the necessity to provide the most accurate diagnosis possible for a process plant criticality is somehow intrinsic in its functioning. Continuous monitoring is a possible way for early detection. However, it is somehow fundamental to be able to actually simulate failures. Reproducing the issues remotely allows to quantify in advance their consequences, causing literally no real damage. Within this context, signed directed graphs have played an essential role within the years, managing to model with a relatively simple theory diverse elements of an industrial network, as well as the logic relations between them.\\ In this work we present a quantitative approach, employing directed graphs to the simulation and automatic reconfiguration of a fault in a network. To model the typical operation of industrial plants, we propose several additions with respect to the standard graphs: 1. a quantitative measure to control the overall residual capacity, 2. nodes of different categories - and then different behaviors - and 3. a fault propagation procedure based on the predecessors and the redundancy of the system. The obtained graph is able to mimic the behaviour of the real target plant when one or more faults occur. Additionally, we also implement a generative approach capable to activate a particular category of nodes in order to contain the issue propagation, equipping the network with the capability of reconfigure itself and resulting then in a mathematical tool useful not only for simulating and monitoring, but also to design and optimize complex plants. The final asset of the system is provided in output with its complete diagnostics, and a detailed description of the steps that have been carried out to obtain the final realization.

A Graph-based Framework for Complex System Simulating and Diagnosis with Automatic Reconfiguration

TL;DR

The paper tackles fault diagnosis and containment in complex industrial systems by modeling plants as weighted directed graphs and introducing a residual service measure to quantify remaining capacity after faults. It combines shortest-path analytics with a fault-propagation model (SINGLE, AND, OR) and employs SWITCH nodes whose states are optimized by genetic algorithms to automatically reconfigure the network and limit cascades. Implemented in SAFEX/GRAPE, the approach yields a practical digital twin capable of simulating faults, diagnosing propagation, and guiding reconfiguration decisions. Results on switch-line and random sparse graphs demonstrate improved residual service and reduced cascade with increased SWITCH deployment, underscoring the framework's potential for plant design, monitoring, and optimization.

Abstract

Fault detection has a long tradition: the necessity to provide the most accurate diagnosis possible for a process plant criticality is somehow intrinsic in its functioning. Continuous monitoring is a possible way for early detection. However, it is somehow fundamental to be able to actually simulate failures. Reproducing the issues remotely allows to quantify in advance their consequences, causing literally no real damage. Within this context, signed directed graphs have played an essential role within the years, managing to model with a relatively simple theory diverse elements of an industrial network, as well as the logic relations between them.\\ In this work we present a quantitative approach, employing directed graphs to the simulation and automatic reconfiguration of a fault in a network. To model the typical operation of industrial plants, we propose several additions with respect to the standard graphs: 1. a quantitative measure to control the overall residual capacity, 2. nodes of different categories - and then different behaviors - and 3. a fault propagation procedure based on the predecessors and the redundancy of the system. The obtained graph is able to mimic the behaviour of the real target plant when one or more faults occur. Additionally, we also implement a generative approach capable to activate a particular category of nodes in order to contain the issue propagation, equipping the network with the capability of reconfigure itself and resulting then in a mathematical tool useful not only for simulating and monitoring, but also to design and optimize complex plants. The final asset of the system is provided in output with its complete diagnostics, and a detailed description of the steps that have been carried out to obtain the final realization.
Paper Structure (12 sections, 3 equations, 5 figures, 4 tables)

This paper contains 12 sections, 3 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Other section
  3. Graph definitions
  4. The system graphs
  5. Graph residual service
  6. Fault propagation
  7. A fault simulation example
  8. Switch activation: a generative approach
  9. Numerical results
  10. Switch line
  11. Random graphs
  12. Conclusions

Figures (5)

  • Figure 1: Shortest Path. In this weighted digraph $G(N,E)$ the shortest path is indicated in green, with respect to the red path, which implies a larger weighted distance between the nodes.
  • Figure 2: Example graph. The four different color identify different areas. Nodes are labeled as $SOURCE$ (reverse triangle), $HUB$ (circle) or $USER$ (up triangle), while the edges can describe $OR$, $SINGLE$, or $AND$ relations between linked nodes. $SWITCH$ nodes (cross) are a particular type of $HUB$ nodes. Nodes with no transparency are passive resistant nodes.
  • Figure 3: Example of a fault event, the damage of one node, namely $SOURCE$$1$. On top, the integer graph, while the damaged one at bottom. $S_{node1}$ and $S_{node15}$ represent the service provided by nodes $1$ and $15$, before and after the perturbation.
  • Figure 4: Graphical sketch of crossover and mutation procedures.
  • Figure 5: Switch line. This graph is divided in five areas, which are identified by the different color. Nodes are labeled as $SOURCE$ (down triangle), $HUB$ (circle), $SWITCH$ (cross) or $USER$ (up triangle), while the edges can describe $OR$, $SINGLE$, or $AND$ relations between linked nodes. Nodes with no transparency are passive resistant nodes.