## 7 Remaining Useful Life Estimate  
Predictive maintenance is a maintenance approach that uses predictive mathematical-statistical models, typically based on data recorded by sensors, to detect anomalies, identify the quantity and quality of damage/degradation, and estimate the remaining useful life (RUL). Figure 13 shows a simple flowchart for RUL estimation. In Figure 13, the first step is to collect data from the monitored system. Then, the raw data are pre-processed to feed into a damage detection algorithm (this step can be based on ML, among others). In this step, different techniques can be implemented, both traditional and AI techniques, to detect anomalies, classify the type of anomalies or damage, quantify and localize the damage, and estimate the remaining lifetime of the structure. It is advantageous to collect as large and heterogeneous a dataset as possible. This is achieved by collecting data under different operating conditions, such as environmental conditions, which allows the development of a more robust algorithm. In civil engineering, representative damage data are hardly available. Therefore, a mathematical model can be developed to predict system response as a function of parameters and environmental conditions. Such response signals are called synthetic signals and should be integrated with the recorded data of the real structure. When the desired amount of real data is not available, integration between real data (undamaged structure) and simulated data (damaged structure) is generally sought. The real data are affected by measurement errors due to the measurement infrastructure, while the simulated data are affected by model errors due to simplifications in the mathematical description of the physical phenomenon. Once the data are recorded or simulated, the next step (Figure 13) is to preprocess them to facilitate the identification of health indicators. This step could be based on one or more techniques, such as noise removal, outlier elimination, dummy trend elimination, frequency domain transformation, and many others. The next step is to identify the structural health by calculating and comparing features that respond to the type of degradation/damage analyzed. These features are used to distinguish a healthy operation from a damaged one. In the  
Figure 12: Variability of accuracy. Figure 13: Flowchart for the remaining useful life estimation algorithm. present work, the last and the previous steps are performed by applying AI. Finally, the last two steps in Figure 13 define a relationship between the health status estimated by the AI and the aging path of the structure, by allowing one to estimate the remaining useful life (RUL) for the structure by imposing a minimum safety threshold and, thus, defining maintenance schedules. The RUL is defined as the time between the current situation and the minimum performance threshold established for the structural system. Depending on the situation, the time may be expressed in days, flights, cycles, among others. For civil engineering works, the RUL is specified in years. Algorithms for RUL calculation can be divided into three categories: similarity algorithms, survival algorithms, and degradation algorithms. Figure 14 shows the different methods for calculating RUL. The choice of the most effective method depends on the system and the available data. The degradation model method is used when undamaged state data are available and a safe threshold can be defined. It is possible to use this information to update a mathematical model of degradation to a performance indicator and then use the history recorded up to that point to predict how the indicator will change in the future. In this way, it is possible to statistically estimate the remaining time before the indicator reaches the imposed threshold and, thus, the RUL. A linear degradation model can be used for this purpose if the system does not experience cumulative degradation. The mathematical model describes the physical process of degradation as a stochastic linear process.