Virtual sensing enables estimation of stress in unmeasured locations of a system using a system model, physical sensors and a process model. The system model holds the relationship between the physical sensors and the desired stress response. A process model processes both the physical sensors and the system model to synthesise virtual sensors that ‘measure’ the desired stress response. Thus, virtual sensing enables mapping between the physical sensors (input) and the desired stress response (output). The system model is a mathematical model of the system based on knowledge or data of the system. Here, the data‐driven system model is constructed directly on data analyses for the specific system. In this paper, supervised learning and data‐driven system models are applied to strain estimation of an offshore wind turbine in the dynamic range through a novel use of principal component analysis (PCA); 40 min of training data is used to establish the data‐driven system model that can estimate the dynamic strain response with high precision for 2 months, while the estimated fatigue damage averaged out to −1.76% of the measured strain response.

When performing vibration tests on structural systems, engineers face the challenge of extracting the dynamic properties from the measured data in an accurate and robust manner. Though several methods exist for this purpose, in some circumstances, they fail to provide clear estimates for these properties, particularly when applied to noise-contaminated data. Here we propose a robust and accurate method formulated in frequency-domain modal model for extracting dynamic properties from vibration data. The method is applied to three application examples, namely the vibrations simulated with the aid of a finite element model and the real-life vibration measurements of a platform specimen and of a full-scale concrete heritage court building. Its performance is thereafter assessed by the so-called stabilization diagrams, the relative error between estimated and exact properties, the modal assurance criterion, and by comparing the synthesized frequency functions to their measured counterparts. This assessment shows that the proposed approach tends to provide clearer and more accurate identification results than those from the state-of-the-art identification methods.

The Ibrahim time domain (ITD) identification technique was one of the first techniques formulated for multiple output modal analysis based on impulse response functions or general free decays. However, the technique has not been used much in recent decades due to the fact that the technique was originally formulated for single input systems that suffer from well-known problems in case of closely spaced modes. In this paper, a known, but more modern formulation of the ITD technique is discussed. In this formulation the technique becomes multiple input by adding some Toeplitz matrices over a set of free decays. It is shown that a special participation matrix can be defined that cancels out whenever the system matrix is estimated. The participation matrix becomes rank deficient if a mode is missing in the responses, but if any mode is present in one of the considered free decays, the participation matrix has full rank. This secures that all modes will be contained in the estimated system matrix. Finally, it is discussed how correlation functions estimated from the operational responses of structures can be used as free decays for the multiple-input ITD formulation, and the estimation errors of the identification technique are investigated in a simulation study with closely spaced modes. The simulation study shows that the multiple-input formulation provides estimates with significantly smaller errors on both mode shape and natural frequency estimates.