Parametric Symbolic Regression for Discovering Unified Crack Growth Models from Diverse Experiments

Since the introduction of the Paris law, considerable efforts have been devoted to developing more accurate and generalized crack growth models to better support damage tolerance design of aeronautical structures. However, derived mechanism-driven models tend to become increasingly complex as more factors are incorporated, while data-driven models tailored to specific datasets often lack cross-condition generalizability. This study addresses this challenge by introducing a novel parametric symbolic regression (PSR) framework, wherein parametric models share a common mathematical structure with condition-adaptive parameters and are optimized by a multi-objective genetic algorithm guided by multicriteria evaluation metrics. Taking the learning of unified crack growth models for metallic materials as a representative case study, we showcase PSR’s capabilities by learning models directly from the Federal Aviation Administration’s database, and the discovered model matches the classic NASGRO model’s performance with much fewer parameters and enhanced interpretability. Moreover, PSR’s efficacy surpasses existing data-driven approaches to discover formulas that accommodate variable experimental conditions and offer high accuracy, interpretability, and parameter stability, highlighting its potential for broader scientific and engineering applications requiring unified models.