Quantifying the Required Sample Size for Desired Confidence in Damage Detection of Structural Health Monitoring

Abstract

In the Structural Health Monitoring (SHM) context, the most critical question is often: Is the system damaged or not? Methods to detect damage rely on identifying novelties in the system response, where significant deviations from training data indicate structural damage. However, this process depends on a threshold, typically defined as a single crisp value based on data distribution or representativeness assumptions. If natural variability, i.e. aleatory uncertainty, is not fully captured, false positives may occur. Probabilistic approaches address aleatory uncertainty, while epistemic uncertainty – arising from lack of knowledge and imprecision – is often modelled using set theory, including interval, fuzzy sets, and other imprecise probability frameworks. Recent research suggests that integrating both types of uncertainty enhances confidence in structural integrity assessments, and fuzzy probabilities offer one feasible approach. This study develops a methodology using fuzzy probabilities to determine the required sample size for a predefined confidence level in damage detection. The fuzzy membership function aggregates plausible intervals into a unified framework, including quantifying how many samples are needed to achieve a certain confidence level. A two-degreeof- freedom system validates the approach, demonstrating its effectiveness in detecting damage compared to a crisp value-based threshold.