Modeling and simulation have been extensively used to solve a wide range of problems in structural engineering. However, many simulations require significant computational resources, resulting in exponentially increasing computational time as the spatial and temporal scales of the models increase. This is particularly relevant as the demand for higher fidelity models and simulations increases. Recently, the rapid developments in artificial intelligence technologies, coupled with the wide availability of computational resources and data, have driven the extensive adoption of machine learning techniques to improve the computational accuracy and precision of simulations, which enhances their practicality and potential. In this paper, we present a comprehensive survey of the methodologies and techniques used in this context to solve computationally demanding problems, such as structural system identification, structural design, and prediction applications. Specialized deep neural network algorithms, such as the enhanced probabilistic neural network, have been the subject of numerous articles. However, other machine learning algorithms, including neural dynamic classification and dynamic ensemble learning, have shown significant potential for major advancements in specific applications of structural engineering. Our objective in this paper is to provide a state-of-the-art review of machine learning-based modeling in structural engineering, along with its applications in the following areas: (i) computational mechanics, (ii) structural health monitoring, (iii) structural design and manufacturing, (iv) stress analysis, (v) failure analysis, (vi) material modeling and design, and (vii) optimization problems. We aim to offer a comprehensive overview and provide perspectives on these powerful techniques, which have the potential to become alternatives to conventional modeling methods.

In this paper, two high-order finite element models are investigated for the solution of two-dimensional wave problems governed by the Helmholtz equation. Plane wave enriched finite elements, developed in the Partition of Unity Finite Element Method (PUFEM), and high-order Lagrangian-polynomial based finite elements are considered. In the latter model, the Chebyshev-Gauss-Lobatto nodal distribution is adopted and the approach is often referred to as the Spectral Element Method (SEM). The two strategies, PUFEM and SEM, were developed separately and the current study provides data on how they compare for solving short wave problems, in which the characteristic dimension is a multiple of the wavelength. The considered test examples include wave scattering by a rigid circular cylinder, evanescent wave cases and propagation of waves in a duct with rigid walls. The two approaches are assessed in terms of accuracy for increasing SEM order and PUFEM enrichment. The conditioning, discretization level, total number of storage locations and total number of non-zero entries are also compared

The determination of structural dynamic characteristics can be challenging, especially for complex cases. This can be a major impediment for dynamic load identification in many engineering applications. Hence, avoiding the need to find numerous solutions for structural dynamic characteristics can significantly simplify dynamic load identification. To achieve this, we rely on machine learning. The recent developments in machine learning have fundamentally changed the way we approach problems in numerous fields. Machine learning models can be more easily established to solve inverse problems compared to standard approaches. Here, we propose a novel method for dynamic load identification, exploiting deep learning. The proposed algorithm is a time-domain solution for beam structures based on the recurrent neural network theory and the long short-term memory. A deep learning model, which contains one bidirectional long short-term memory layer, one long short-term memory layer and two full connection layers, is constructed to identify the typical dynamic loads of a simply supported beam. The dynamic inverse model based on the proposed algorithm is then used to identify a sinusoidal, an impulsive and a random excitation. The accuracy, the robustness and the adaptability of the model are analyzed. Moreover, the effects of different architectures and hyperparameters on the identification results are evaluated. We show that the model can identify multi-points excitations well. Ultimately, the impact of the number and the position of the measuring points is discussed, and it is confirmed that the identification errors are not sensitive to the layout of the measuring points. All the presented results indicate the advantages of the proposed method, which can be beneficial for many applications.

We introduce the augmented Tikhonov regularization method motivated by Bayesian principle to improve the load identification accuracy in seriously ill-posed problems. Firstly, the Green kernel function of a structural dynamic response is established; then, the unknown external loads are identified. In order to reduce the identification error, the augmented Tikhonov regularization method is combined with the Green kernel function. It should be also noted that we propose a novel algorithm to determine the initial values of the regularization parameters. The initial value is selected by finding a local minimum value of the slope of the residual norm. To verify the effectiveness and the accuracy of the proposed method, three experiments are performed, and then the proposed algorithm is used to reproduce the experimental results numerically. Numerical comparisons with the standard Tikhonov regularization method show the advantages of the proposed method. Furthermore, the presented results show clear advantages when dealing with ill-posedness of the problem.