Topology-Driven Fault Detection in Smart Cities

Topology-Driven Fault Detection in Smart Cities: Utilizing Dynamic Graph Filtrations and Persistent Homology for IoT Connectivity Patterns

Shrishti Rastogi / Research Article

Abstract: The rapid proliferation of IoT devices in smart cities necessitates robust, real-time monitoring systems to detect infrastructure faults. Traditional graph-theoretic methods often fail to capture multi-scale structural changes under fluctuating environmental conditions. This paper presents a topology-driven framework utilizing Topological Data Analysis (TDA), specifically persistent homology, to analyze time-varying graph filtrations of IoT connectivity patterns. We integrate Distance-to-Measure (DTM) filtrations to mitigate noise, coupled with machine learning classifiers applied to stable topological summaries. Empirical evaluation on simulated smart city datasets demonstrates superior F1-scores in detecting network fragmentation events.

1. Introduction

Modern smart cities rely on continuous IoT sensor operations. When a systemic fault occurs—such as a localized power outage—the underlying manifold of the network topology undergoes abrupt structural deformations. Traditional spectral methods often miss these changes because average node degrees may remain stable, whereas homological connectivity features shift immediately.

2. Mathematical Formalization & Methodology

We define the sensor network as a time-varying graph G_t = (V_t, E_t, w_t). To mitigate noise, we define the Distance-to-Measure (DTM) function for point cloud X and mass parameter 0 < m ≤ 1:

d_{X,m}(y) = infS ⊆ X, μ(S) ≥ m supx ∈ S ||y - x||

Explicit Mapping of Topology to Faults

• H₀ (Connected Components): Spikes or drops imply network fragmentation or district power outages.
• H₁ (Loops/Cycles): Sudden death indicates failed redundant paths; birth indicates routing loops.
• H₂ (Voids): Indicates spatial coverage gaps in 3D municipal infrastructures.

3. Experiments and Results

Using Python (Ripser and NetworkX), we evaluated our DTM-TDA pipeline against baseline spectral methods on a 120-node dynamic IoT graph.

Method	Precision	Recall	F1-Score
Baseline Spectral Clustering	0.76	0.68	0.72
Standard Vietoris-Rips + ML	0.82	0.79	0.80
Proposed DTM-TDA Pipeline	0.91	0.89	0.90

4. Discussion & Ethical Considerations

Because TDA relies on connectivity shapes rather than payload data, it inherently preserves payload privacy. However, individual connectivity loops could theoretically be tracked, necessitating proper anonymization.

5. Conclusion

The proposed topology-driven framework bridges abstract TDA theory and actionable smart city infrastructure monitoring, offering superior resilience against sensor noise and transient outliers.