## 8 Case Study Application
In contrast, the estimation before 10 to 15 years and after 40 years is unreliable, but not problematic, if we consider the nature of the phenomenon: in the early years of the structure's life, the algorithm will learn and update itself to detect the physiological degradation trend of the structure (of course, in the case of damage/pathological degradation, there is always an AI that can provide us with a snapshot of the current damage state), and, in this time frame, it is less relevant to estimate the RUL; analogously,  
Figure 16: Damage estimation by AI as time passes. in the last moments of the structure life, it is obviously useless to estimate the RUL, since the damage identification AI will report damage close to the imposed threshold. Instead, in the intermediate life span, it is important to make an accurate RUL estimate in order to detect and locate future damage and have enough time to effectively plan maintenance actions. However, it is interesting to note that the estimated RUL is practically always lower than the actual RUL, i.e., it underestimates the actual RUL. From a structural safety perspective, it is certainly better to be in this state than in the opposite state, i.e., overestimating the RUL. From a mathematical point of view, this is due to two factors: the degradation model used is exponential, and a penalty matrix was used in the AI training. The exponential degradation model, even if updated, will always provide a shorter remaining life than a linear degradation model due to its curvature. From the authors' point of view, it is not recommended to use a linear model: first, because underestimating the RUL is beneficial for structural safety, and second, because it is not possible to know the shape of the degradation function a priori. Thus, if we use a linear degradation model and the degradation function turns out to be exponential, we would overestimate the RUL to the detriment of safety. At the same time, the introduction of the penalty matrix in the AI training phase leads to a higher probability of overestimating damage, which in turn leads to an underestimation of the RUL. One aspect that could have a strong impact on RUL is the discontinuity of the damage estimated by the AI, as shown and discussed in Figure 16, due to the solution of a classification problem. Future developments in this regard could include methods to reduce the discontinuity of damage estimation so that a more faithful reconstruction of the degradation history is available. Another solution could be to implement techniques for interpolating or averaging the damage classes resulting from AI to facilitate the RUL update algorithm. A hypothesis on the possible use of RUL calculation throughout the life cycle of the structure is presented in Figure 18. All the techniques developed and presented in this paper are designed for estimating the remaining useful life. Once the construction of the structure is completed and the monitoring infrastructure is properly installed, it is possible to update the FE model based on the recorded data (FE model, which could end up being the same model used for the design of the structure). In this way, we obtain the FE model needed for the AI training. This FE model will undoubtedly be more accurate than an outdated model as a result of the optimization problem. In this way, we will minimize the model error in the AI that will be trained with the signals derived from this FE model. Figure 17: Estimated RUL. Once the training phase is complete, we will have an AI that can estimate the damage (with some accuracy and therefore uncertainty in the estimate) and we can use this information as input for estimating the remaining useful life. At this point, every time we perform a registration, we will estimate the damage over the previously trained AI and iteratively update the RUL calculation. Finally, the possibility of extending the proposed framework to real structures involves additional considerations.