In recent decades, nonlinear damping identification (NDI) in structural dynamics has attracted wide research interests and intensive studies. Different NDI strategies, from conventional to more advanced, have been developed for a variety of structural types. With apparent advantages over classical linear methods, these strategies are able to quantify the nonlinear damping characteristics, providing powerful tools for the analysis and design of complex engineering structures. Since the current trend in many applications tends to more advanced and sophisticated applications, it is of great necessity to work on developing these methods to keep pace with this progress. Moreover, NDI can provide an effective and promising tool for structural damage detection purposes, where the changes in the dynamic features of structures can be correlated with damage levels. This review paper provides an overview of NDI methods by explaining the fundamental challenges and potentials of these methods based on the available literature. Furthermore, this research offers a comprehensive survey of different applications and future research trends of NDI. For potential development and application work for nonlinear damping methods, the anticipated results and recommendations of the current paper can assist researchers and developers worldwide to find out the gaps and unsolved issues in the field of NDI.

Structural damage inspection is a key structural engineering technique that strives for ensuring structural safety. In this regard, one of the major intelligent approaches is the inverse analysis of structural damage using evolutionary computation. By considering the recent advances in this field, an efficient hybrid objective function that combines the global modal kinetic and modal strain energies is introduced. The newly developed objective function aims to extract maximum dynamic information from the structure and overcome noisy conditions. Moreover, the original methods are usually vulnerable to the associated high multimodality and uncertainty of the inverse problem. Therefore, the oppositional learning (OL) for population initialization and convergence acceleration is first adopted. Thereafter, the unified particle swarm algorithm (UPSO) mechanism is combined with another newly developed algorithm, the gradient-based optimizer (GBO). The new algorithm, called the oppositional unified particle swarm gradient-based optimizer (OL-UPSGBO), with the convergence acceleration feature of (OL), enhances balanced exploration-exploitation of UPSO, and the local escaping operator of GBO is designed to specifically deal with the complex inverse analysis of structural damage problems. To authenticate the performance of the OL-UPSGBO, the complex benchmark set of CEC 2017 is adopted to compare the OL-UPSGBO with several original metaheuristics. Furthermore, the developed approach for structural damage identification is tested using several damage scenarios in a multi-story frame structure. Results show that the developed approach shows superior performance and robust behavior when tackling the inverse analysis of structural damage.

The output response of any intact oscillatory system subjected to a Gaussian excitation is also Gaussian in nature. On the contrary, when the system contains any type of underlying nonlinearity, the output signal is definitely non-Gaussian. In beam structures, the presence of fatigue-breathing cracks significantly influences the dynamic response characteristics under Gaussian excitation. The presence of such cracks alters the response to be nonlinear, and the non-Gaussianity of the system will arise. In order to examine the non-Gaussianity features and ability for the detection and localization of fatigue cracks, several breathing crack identification scenarios in beam-like structures are presented in this paper. The effects of single and multiple breathing cracks corresponding to different boundary conditions on the responses of beams are studied. The results are analyzed based on the higher-order time-domain transformations. Higher-order transformations, namely the skewness and kurtosis coefficients in addition to the Shannon entropy, are exploited to provide dynamic details about the response, which the conventional second-order statistics cannot show. The results exhibit that the proposed methods are robust and immune to noise and can detect and localize breathing cracks with different sensitivities.

Cracks and other damages generated during the service of bridges can reduce the load bearing capacity and threaten operational safety.Finite Element Model Updating (FEMU), as one of the important means of structural health diagnosis, identifies structural damage through changes in model parameters. The three key factors of FEMU are updating variables, objective functions, and optimization algorithms. The poor selection of the above three factors in existing research leads to high calculation errors in model updating, and inevitably lead to the inability of the finite element model to carry out structural health monitoring, affecting the normal operation of the structure. In order to solve the above problems, this paper combines previous research and establishes a model updating algorithm based on the combination of eigenvector difference approach and particle swarm optimization (ED-PSO). The validity and accuracy of this method are verified by finite element analysis of a simply supported beam. Compared with the existing model updating algorithms based on the combination of static and dynamic methods and particle swarm optimization (CSD-PSO), the results show that the proposed ED-PSO model updating algorithm has higher accuracy and is expected to be better applied to bridge finite element model updating research.