Fuzzy-Logistic Models for Incorporating Epistemic Uncertainty in Bridge Management Decisions

Many bridge management systems (BMSs) plan future maintenance and inspection based on deterioration models derived from probabilistic analysis of field inspection data. Such analysis considers the aleatoric but not the epistemic uncertainty arising from subjective or imprecise data. This raises questions regarding the efficiency and safety of maintenance and inspection decisions. Several methodologies have been proposed to address both uncertainties; however, they tend to be taxing in terms of inspection data requirements. Thus, this work proposes a new BMS-compatible methodology to derive deterioration models using logistic regression to capture aleatoric uncertainty and fuzzy set theory to capture epistemic uncertainty. To formulate the models, subjective or imprecise data, such as bridge condition rating, is modeled using membership functions, rather than discrete values, and then integrated into logistic regression analysis. This results in logistic models with fuzzy coefficients. The proposed fuzzy-logistic models can be used to predict a range of possible future bridge conditions, rather than a discrete condition and hence lead to a range of possible management strategies that can be then optimized using life-cycle cost analysis. The application of the proposed framework is demonstrated through a case study.