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Given the random vibration of a linear and time-invariant system, the correlation function matrix is equivalent to free decays when the system is excited by Gaussian white noise. Correlation-driven Operational Modal Analysis utilises these properties to identify modal parameters from systems in operation based on the response only. Due to the finite length of the system response, the correlation function matrix must be estimated and this introduces statistical errors. This article focuses on the statistical errors due to this estimation process and the effect it has on the envelope and zero crossings of the estimated correlation function matrix. It is proven that the estimated correlation function matrix is a Gaussian stochastic process. Furthermore, it is proven that the envelope of the modal correlation function matrix is Rice distributed. This causes the tail region of the correlation function to become erroneous -called the noise tail. The zero crossings are unbiassed, but the random error related to the crossings increases fast in the noise tail. The theory is tested on a simulated case and there is a high agreement between theory and simulation. A new expression for the minimal time length is introduced based on the bias error on the envelope.

In operational modal analysis, the correlation function matrix is treated as multiple free decays from which system parameters are extracted. The finite time length of the measured system response, however, introduces statistical errors into the estimated correlation function matrix. These errors cause both random and bias errors that transfer to an identification process of the modal parameters. The bias error is located on the envelope of the modal correlation functions, thus violating the assumption that the correlation function matrix contains multiple free decays. Therefore, the bias error transmits to the damping estimates in operational modal analysis. In this paper, we show an automated algorithm that reduces the bias error caused by the statistical errors. This algorithm identifies erratic behaviour in the tail region of the modal correlation function and reduces this noise tail. The algorithm is tested on a simulation case and experimental data of the Heritage Court Building, Canada. Based on these studies, the algorithm reduces bias error and uncertainty on the damping estimates and increases stability in the identification process.

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Fatigue life assessment currently recommended by offshore standards is associated with a large number of uncertainties mainly related to the environmental loads and the numerical model. Recently, for economic reasons, the need for extending the lifetime of existing offshore structures led to the necessity of developing more accurate and realistic predicting models so that damage detection and maintenance can be optimized. This paper proposes the implementation of Structural Health Monitoring Systems in order to extract modal properties—such as mode shapes, natural frequencies, and damping ratios—throughout Operational Modal Analysis (OMA), which is the engineering field that studies the modal properties of systems under ambient vibrations or normal operating conditions. The identified modal properties of the structural system are the fundamental information to update a finite element model by means of an expansion technique. Then, the virtual sensing technique—modal expansion—is used to estimate the stress in the entire structure. Though existing models depend on the load estimation, the model based on OMA-assisted virtual sensing depends on the measured responses and assumes that the loads act as random vibrations. A case study using data from a real offshore structure is presented based on measurements recorded during normal operation conditions of an offshore tripod jacket. From strains estimated using OMA and virtual sensing, fatigue stresses are predicted and verified by applying the concept of equivalent stress range. Both estimated and measured strains are given as input data to evaluate the equivalent stress range and compared with each other. Based on this study, structural health monitoring estimates the fatigue stresses with high precision. As conclusion, this study describes how the fatigue can be assessed based on a more accurate value of stress and less uncertainties, which may allow extending the fatigue life of offshore platforms.