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The conventional modal strain energy (MSE), as a practical objective function, suffers from the lack of access to the damaged stiffness matrix and uses the intact stiffness matrix of the structure instead. To overcome the aforementioned deficiency of the MSE, this study proposes a reformed elastic strain energy-dissipation criterion called the "augmented modal strain energy" (AMSE) which is composed of relative differences of natural frequency and mode shape. In the AMSE not only the effects of the energy-dissipation criterion as a function of natural frequency but also the equilibria of the elastic strain energy as a function of mode shape are considered. Hereupon, the AMSE is implemented along with the interactive autodidactic school (IAS) optimization algorithm to investigate the effectiveness of the proposed identification method. In this regard, the AMSE is verified by assessing three benchmark truss and frame structures. The obtained results confirm the reliable performance of AMSE in both terms of intensification and diversification. Furthermore, it is observed that despite using noise-polluted modal data, the proposed AMSE not only identifies the damage location accurately, but also anticipates the extent of damage precisely. Consequently, the proposed energy-dissipation-based objective function (AMSE) is suggested, along with the IAS optimization algorithm, as a robust technique for the damage detection of structures. [ABSTRACT FROM AUTHOR]

• A novel multistage probabilistic methodology called the RBST is proposed. • The RBST was examined on three benchmark structures by taking uncertainties. • Results show that the proposed technique has strong noise immunity and robustness. • The RBST shows a good performance in terms of the probability of damage existence. A novel multistage probabilistic methodology called the "Reliability-Based Sieve Technique (RBST)" is presented in this paper for the reliable assessment of the functionality of structures. In this method, the structural damage detection problem is defined as a multistage probabilistic optimization problem. The Holistic Objective Function (HOF) based on the combination of the inherent characteristics of the structure (i.e., the vibration frequencies and mode shapes) is incorporated into the Interactive Autodidactic School (IAS) optimization algorithm, for the first time, to solve the problem. In addition, the Latin Hypercube Sampling (LHS) technique is used to simulate and analyze the probabilistic damage assessment problem. In each stage of the proposed methodology, the Probability of Damage Existence (PDE) is computed in each of the structural elements through a probabilistic damage detection analysis. According to the results of the PDE in the structural elements in each stage, the elements with low PDEs are gradually sieved in the subsequent steps. The sifted elements in each stage are considered as intact ones in the next stage. This systematic filtration of the design variables can simultaneously decrease the dimensions and increase the speed of the optimization problem. To improve the performance of the RBST, the sizes of the sieves are regularly reduced for the next stages. This multistage procedure is continued until convergence to a precise structural damage location diagnosis and intensity prognosis is achieved. Finally, to investigate the efficiency and robustness of the proposed technique, it is examined on three benchmark structures by taking the high level of uncertainties associated with both finite element modeling errors and vibration data noises into account. The obtained results confirmed that the proposed technique correctly identifies the damage indices and has consummate capability compared with the single-stage probabilistic analysis. Likewise, it is observed that the RBST accurately sieves the intact elements from the vector of the design variables in highly noisy conditions. Consequently, in the presence of both mentioned uncertainty sources, the RBST not only assesses the damage site and extent properly, but also shows a reliable performance in terms of PDE. [ABSTRACT FROM AUTHOR]

In this work, we propose a procedure to estimate the Minimum Observable Damage (MOD) by a vibration-based Structural Health Monitoring (SHM) system. The MOD is defined as the smallest damage size that can be detected by an SHM system with given Probability of Detection (POD) and Probability of False Alarm (PFA). To this purpose, the MOD is computed by exploiting the Receiver Operating Characteristic (ROC) analysis, once a damage index (DI) built on monitoring data/features is defined. In particular, the MOD is defined as the damage intensity corresponding to an area under the ROC curve of 95%. The proposed idea is discussed by utilizing pseudo-experimental data generated via numerical simulations for undamaged and damaged structures. In the developed simulations, environmental uncertainties and measurement noises are considered. As case studies, we consider truss structures and use modal data, namely frequencies of vibrations and mode shapes, to build the DIs. Using the dataset of DIs, the ROC methodology is exploited to establish the probability of detecting certain damage over the probability of false alarms. For a given DI, results are provided in terms of MOD for each structural element of the truss structure considering one damaged element at a time. By establishing a relation between modal data, damage size, and POD/PFA, the proposed approach can assess the quality of the adopted DI, thus supporting the initial design of an SHM system. [ABSTRACT FROM AUTHOR]