## 9 Conclusions  
This paper proposed and investigated a framework for estimating structural damage using machine learning techniques (ML) and the resulting remaining and useful life (RUL). The applied ML technique involves supervised training, so knowledge of the data for the undamaged and especially for the damaged structural system is required. Considering the uniqueness of civil structural systems, training data for the different damage classes are not available. Therefore, a hybrid-based approach was adopted here: a FE model is used as a digital twin to generate synthetic damage data. The proposed, implemented, and numerically tested framework seems to be able to estimate, quantify, and localize the damage (in this case the corrosion thickness of a reference steel column) in a robust, reliable way and with very good accuracy. A reliable estimate of actual damage is a necessary prerequisite for RUL assessment. In this context, a framework for updating the RUL of a structural system has been proposed and investigated. To achieve this, a Bayesian approach is adopted for updating the parameters of the chosen exponential degradation model with random coefficients. After updating the degradation model, it is possible to determine the updated a posteriori distribution of RUL of the structure. Finally, the framework was numerically applied to the reference case study, with the trained AI serving as the basis for the probabilistic estimation of the current state of health. The main scientific contributions in this research are the development of an innovative framework that allows a damage estimation AI to interoperate with the probabilistic RUL estimation model. The application of the framework to a numerical, albeit simple, structural system allowed validating the soundness of the method. Therefore, the added value of performing a Bayesian update of the parameters to properly incorporate the information into the RUL estimation model is significant. In solving a supervised learning problem, such as the one presented in this paper, a fundamental and crucial aspect becomes clear: do we have data about the damaged structure (for all types and severities of damage)? If the answer is no, which is usually the case, one needs to find a way to estimate it. In this paper, we attempted to solve a supervised learning problem by developing a general framework that uses numerical FE modeling to produce synthetic data of the monitored structure. Of course, these data will be affected by model errors due to the various assumptions made in the development of the model itself. For this reason, we refer to this technique as hybrid-based: an AI model is created from the data all or part of which can be artificially generated by numerical simulations. To limit, but not to eliminate model errors, finite element model update (FEMU) techniques can be used to update the FE model before generating the synthetic data. In this way, model errors are minimized for a newly built structure, but, more importantly, the developed ML method could be used to monitor existing structures, thus already showing some degradation (whether physiological or pathological), in which case it would be strongly discouraged to proceed with AI training with a model representing the undamaged structure. Another important point to consider when monitoring a structural system is its sensitivity to environmental conditions (e.g., temperature and humidity sensitivity, among others). Such conditions can cause features to change in a way that exceeds the change caused by potential damage. For civil engineering structures, such as bridges, mass can also have a significant effect on the modal properties of the infrastructure. Indeed, for these structures, variable loads and thus variable masses could be an important part of the loading on the whole structure. In the proposed framework, these random conditions are integrated into the mass parameter, which is randomly chosen and not included as a known parameter in the learning process.