PSI - Issue 84

F. Foria et al. / Procedia Structural Integrity 84 (2026) 645–652

646

Keywords: bridges; structural monitoring; infrastructure maintenance; structural identification; vibration analysis; OMA

1. Introduction The progressive ageing of Italy's building stock over the years has led to increasing attention being paid to the preservation of buildings, partly as a result of numerous structural collapses involving serious loss of life. In the field of scientific research, new and efficient methodologies have been developed, based on the dynamic identification of the structure, which allow for the early detection of structural damage. Significant variations in the modal parameters of a structure, i.e. in frequencies, damping and modal deformations, are indicative of variations in mass, or more frequently in stiffness, and are therefore indicators of material damage or geometric instability. Structural monitoring, combined with periodic or permanent verification of dynamic properties, allows prompt action to be taken to limit risk conditions, inhibiting or limiting, when necessary, the use of the structure through the activation of various levels of alarm. The constant identification of modal parameters also allows for the calibration and updating of numerical models, such as finite element models, by comparing the results of modal analysis with the results obtained from field measurements. These are generally recordings of accelerations and/or velocities of notable points on the structure under operating conditions or subject only to environmental actions. Identification methodologies based on discrete or continuous readings over time of accelerations due to environmental actions, fall within the framework of Operational Modal Analysis (OMA). They offer certain advantages, such as low cost, since the equipment for discrete readings is not dedicated to the structure and can be reused in other contexts, and the mathematical robustness of the signal processing and interpretation procedures. However, the method is strongly influenced by background noise in the recordings. The application of ad hoc filters is necessary and, in some cases, the output remains challenging to interpret. Furthermore, linearity, stationarity of the structural response and the assumption that excitation can be modelled as white noise must be satisfied. This paper presents an algorithm for the automatic identification of the modal parameters of a structure based on raw accelerometer measurement data, acquired continuously or occasionally over time. An easy-to-use user interface allows data management and interpretation even for operators who are not experts in the field of dynamic identification. The algorithm is based on the Stochastic Subspace Identification (SSI) methodology. Within the SSI family, there are two different methods: the Covariance driven Stochastic Subspace Identification (SSI-COV) method, which requires that covariance functions are firstly estimated from raw response data, and the Data driven Stochastic Subspace Identification (SSI-DATA) method, where raw data are collected in the Henkel matrix, using the QR decomposition to project the future data onto the past data’s subspace, identifying the system dynamics In the SSI-COV method, utilized in this study, response data are processed into covariance functions. Then, state space models are solved and the singular value decomposition combined with the stabilization diagrams (SD) with clustering to pinpoint stable modes are used to identify structural frequencies. The procedure relies on a number of parameters that must be defined by the user. Apart those related to thresholds, whose values are defined within reasonable ranges, the effective determination of the modal parameters strongly depends on two important parameters of SSI-COV method, namely the model order of the structural system and of the time lag . The model order refers to the number of modes (or states) chosen to represent the vibrating structure. The time lag defines the size of the covariance matrix, that is how the algorithm has to look far back in time for correlations to identify the system's modal parameters from vibration data. Modal parameters (frequency, damping) are identified using SD looking for stable poles. If the order of the model is too small, relevant modes can be missed, while excessively increasing it may include spurious modes that fluctuate wildly due to the presence of noise in the signal [1] [2]. A right choice of the time lag involves balancing computational cost, noise reduction, and capturing the actual dynamic response. In addition, a large time lag may lead to bad conditioned covariance matrices, introducing large errors in the calculation. The determination of these parameters should be performed using SD or automated criteria to find stable modes [1] [3]. The paper describes an automatic procedure for the optimal selection of the two aforementioned parameters. It also describes the entire algorithmic process, illustrated through its application to a simple model and a case study.