Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

FedAvg-Based CTMC Hazard Model for Federated Bridge Deterioration Assessment

Takato Yasuno

Abstract

Bridge periodic inspection records contain sensitive information about public infrastructure, making cross-organizational data sharing impractical under existing data governance constraints. We propose a federated framework for estimating a Continuous-Time Markov Chain (CTMC) hazard model of bridge deterioration, enabling municipalities to collaboratively train a shared benchmark model without transferring raw inspection records. Each User holds local inspection data and trains a log-linear hazard model over three deterioration-direction transitions -- Good$\to$Minor, Good$\to$Severe, and Minor$\to$Severe -- with covariates for bridge age, coastline distance, and deck area. Local optimization is performed via mini-batch stochastic gradient descent on the CTMC log-likelihood, and only a 12-dimensional pseudo-gradient vector is uploaded to a central server per communication round. The server aggregates User updates using sample-weighted Federated Averaging (FedAvg) with momentum and gradient clipping. All experiments in this paper are conducted on fully synthetic data generated from a known ground-truth parameter set with region-specific heterogeneity, enabling controlled evaluation of federated convergence behaviour. Simulation results across heterogeneous Users show consistent convergence of the average negative log-likelihood, with the aggregated gradient norm decreasing as User scale increases. Furthermore, the federated update mechanism provides a natural participation incentive: Users who register their local inspection datasets on a shared technical-standard platform receive in return the periodically updated global benchmark parameters -- information that cannot be obtained from local data alone -- thereby enabling evidence-based life-cycle planning without surrendering data sovereignty.

FedAvg-Based CTMC Hazard Model for Federated Bridge Deterioration Assessment

Abstract

Bridge periodic inspection records contain sensitive information about public infrastructure, making cross-organizational data sharing impractical under existing data governance constraints. We propose a federated framework for estimating a Continuous-Time Markov Chain (CTMC) hazard model of bridge deterioration, enabling municipalities to collaboratively train a shared benchmark model without transferring raw inspection records. Each User holds local inspection data and trains a log-linear hazard model over three deterioration-direction transitions -- GoodMinor, GoodSevere, and MinorSevere -- with covariates for bridge age, coastline distance, and deck area. Local optimization is performed via mini-batch stochastic gradient descent on the CTMC log-likelihood, and only a 12-dimensional pseudo-gradient vector is uploaded to a central server per communication round. The server aggregates User updates using sample-weighted Federated Averaging (FedAvg) with momentum and gradient clipping. All experiments in this paper are conducted on fully synthetic data generated from a known ground-truth parameter set with region-specific heterogeneity, enabling controlled evaluation of federated convergence behaviour. Simulation results across heterogeneous Users show consistent convergence of the average negative log-likelihood, with the aggregated gradient norm decreasing as User scale increases. Furthermore, the federated update mechanism provides a natural participation incentive: Users who register their local inspection datasets on a shared technical-standard platform receive in return the periodically updated global benchmark parameters -- information that cannot be obtained from local data alone -- thereby enabling evidence-based life-cycle planning without surrendering data sovereignty.
Paper Structure (26 sections, 11 equations, 4 figures, 3 tables, 1 algorithm)

This paper contains 26 sections, 11 equations, 4 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Bridge Deterioration Modelling
  4. Federated Learning
  5. FL for Infrastructure and Structural Health Monitoring
  6. Deterioration Prediction.
  7. Technical Standard Platforms.
  8. FL Benchmarking Platforms.
  9. Problem Formulation
  10. Deterioration State Space and Transitions
  11. Log-Linear Hazard Function
  12. Transition Probabilities over Inspection Interval
  13. Log-Likelihood per Observation Pair
  14. Parameter Space
  15. Federated Learning Design
  16. ...and 11 more sections

Figures (4)

  • Figure 1: Computation flow of the proposed FedAvg-CTMC framework for bridge deterioration benchmark estimation.
  • Figure 2: Four-panel scale comparison for 500, 2,000, and 4,000 Users. Top-left: NLL convergence curves. Top-right: Aggregated gradient norm in log scale. Bottom-left: Beta estimation MAE per transition (grouped bar). Bottom-right: Final-round NLL and $\|\bar{\mathbf{g}}\|$ with wall-clock time.
  • Figure 3: Learning curves for the 4,000-User run (50 rounds, $\rho=10\%$). Top-left: Average NLL per communication round. Top-right: Aggregated gradient norm $\|\bar{\mathbf{g}}_r\|$ in log scale. Bottom-left: Trajectories of 8 $\beta$ coefficients for transitions $0\to1$ and $0\to2$; dashed lines show ground-truth values. Bottom-right: Trajectories of 4 $\beta$ coefficients for transition $1\to2$; dashed lines show ground-truth values.
  • Figure 4: 3$\times$3 covariate-pair heatmaps of benchmark transition probabilities ($\Delta t = 3$ yr, 4,000-User model). Rows: transitions $0\to1$ / $0\to2$ / $1\to2$. Columns: covariate pairs $(z_1,z_2)$ / $(z_1,z_3)$ / $(z_2,z_3)$; the remaining covariate is fixed at 0.5. Colour scale is shared within each row; white contour lines mark iso-probability levels.