# Probabilistic Modeling and Prediction of Continuous FRP Degradation Curves Based on CSDI Diffusion Models

## TL;DR

This paper introduces a new method using CSDI diffusion models to predict the continuous degradation of FRP materials, improving accuracy and reliability under limited data.

## Contribution

The novel probabilistic framework enables continuous FRP degradation curve prediction using CSDI diffusion models.

## Key findings

- CSDI achieves high predictive accuracy with RMSE = 0.332 and R2 = 0.86.
- The method provides robust probabilistic calibration with CRPS = 0.170 at 30% missing data.
- It generates physically consistent performance trajectories from sparse observations.

## Abstract

Traditional FRP durability forecasting predominantly treats performance evolution as a discrete “point-to-point” regression, inherently overlooking temporal coherence and stochastic uncertainty. This study proposes a novel probabilistic framework based on the CSDI diffusion model to reconstruct continuous FRP degradation curves. By formulating long-term forecasting as a conditional imputation task, the methodology generates physically consistent performance trajectories from sparse experimental observations. Results from a multi-factor database demonstrate that CSDI enables a paradigm shift to continuous sequence generation, achieving high predictive accuracy (RMSE = 0.332, R2 = 0.86) and robust probabilistic calibration (CRPS = 0.170) at a 30% missing ratio. This approach establishes a reliable probabilistic risk envelope, providing a scientific tool for the life-cycle reliability assessment of FRP structures under small-sample constraints.