**1. Introduction**

Modern society makes large use of civil infrastructures. Hydroelectric power generation presupposes that dams are built along mountain valleys to store water. River and valleys are crossed by bridges and viaducts, tunnels are built under mountains. Any engineered product, in particular a structure such as a dam or a bridge, has a finite design working life. This means that after a certain amount of time (e.g., half a century), large maintenance works are required, otherwise, the structural safety reduces to unacceptable levels and the infrastructure must be destroyed or abandoned [1]. Large efforts have been made by researchers to understand the phenomena that occur on the infrastructures and the ageing processes acting on the structures, which reduce their bearing capacity [2]. After decades of tests and a larger and solid knowledge base, modern structural design philosophies account for the variability of the loads, the environmental effects on the structure, and the possibility of accidental phenomena (such as earthquakes or fire) and impose strict prescription in construction works to avoid the need of large maintenance works during the expected working life.

Nevertheless, it must be remembered that the larger part of the actual infrastructural heritage was built in the Sixties, and it has had more than fifty years of service. Such structures suffer from two major problems. First, it must be considered that loading and environmental scenarios not accounted for during the design phase could have occurred, thus, the infrastructures can have experienced a quicker ageing process. In fact, this results in costly maintenance or in abandonment before the end of the design working life. Second, the infrastructures cannot be replaced in an economical manner since service inconveniences and high construction costs must be considered before planning the demolition and the subsequent reconstruction [3]. Therefore, to lengthen the working period, a structural health monitoring (SHM) framework must be implemented to detect the location and the extent of damage on structures [3,4].

Briefly, SHM can be implemented through non-destructive or destructive techniques. The former presupposes that continuous or discrete measurements are carried out during a time period and modification of the trends are interpreted as the evolution of the damage. The latter implies that samples of material (concrete, steel, reinforcement bars) are taken from the structure and tested in in laboratories to determine the residual mechanical properties (uniaxial compression strength in concrete, tensile strength in steel) [5]. The resulting information is implemented in numerical finite element (FE) models of the structure, and the structural safety is assessed. Destructive investigations are also required when there is the possibility that components buried in the structure, e.g., post-tensioned tendons, are damaged. Referring to non-destructive methods, many approaches have been formulated, mainly based on the study of the evolution of the dynamical properties (vibration frequencies and damping) of the structure [6,7]. Details on the possible analysis techniques and their pros and cons can be found in the specific literature (see, e.g., [7–9]).

As reported by Farrar and Worden [3], machine learning is a useful tool in SHM as it can provide interesting insights into the following five hierarchical points: (i) detection of the damage, (ii) localization of the damage, (iii) classification of the type of damage, (iv) evaluation of the extent of the damage, and (v) prediction about the residual safety of the structure. Supervised and unsupervised learning approaches can be implemented into a machine learning framework. Referring to the former, it is mandatory that data from every conceivable damage situation should be available. In this sense, all the five points previously enumerated can be implemented into an artificial intelligence framework. In contrast, unsupervised learning can only be adopted for the detection of damage and, sometimes, for the localization of the damage.

The comparison between statistical patterns of recorded data provides information about the structural condition [10,11], provided that a calibration phase on an undamaged structure is performed [12]. Pattern recognition of extracted features has been found e ffective for detecting damages: various artificial intelligence techniques have been proposed, e.g., autoregressive models [13], artificial neural networks [14], or support vector machines [15]. Novelty detection or anomaly detection methods have been also largely adopted; some examples are provided in [16–19].

A recent review paper on the emerging artificial intelligence methods applied in structural engineering was written by Salehi and Burgueno [20]; it concluded that the use of artificial intelligence in feature extraction is a powerful tool in SHM [21].

The current approaches reveal that large datasets are needed to monitor a structure. In particular, to detect a damage, structural information from when the damage was not present is required. This reflects that the knowledge of at least one previous state of the system is needed to check for a change in structural behavior, which can be interpreted through the approaches previously illustrated. Obviously, this is not always possible since, usually, monitoring starts after the appearance of a defect on a structure. This evidence suggests two major problems. On one side, to encompass all the possible types of damage (location, type, and extent), a consistent amount of information related to a large number of monitored structures is required. On the other, adopting unsupervised learning approaches requires long time records on a single structure. The present paper proposes a hybrid approach that helps to address these problems. The method allows for numerical modeling to simulate all the possible damage configurations on a structure and for supervised learning to interpret the records of sensors on a structure. Exploiting just a small part of the power of machine learning algorithms, in the present paper, shallow neural networks (NN) [22] are adopted as learning machines for the analysis. To be implemented in a real case, the fact that the measurements can be a ffected by errors must be included in the analysis. Thus, random errors are included in the analysis.
