A Monte Carlo Simulation Approach in Non-linear Structural Dynamics Using Convolutional Neural Networks

Abstract

The evaluation of the structural response statistics constitutes one of the principal tasks in engineering. However, in the tail region near structural failure, engineering structures behave highly non-linear, making an analytic or closed form of the response statistics difficult or even impossible. Evaluating a series of computer experiments, the Monte Carlo method has been proven a useful tool to provide an unbiased estimate of the response statistics. Naturally, we want structural failure to happen very rarely. Unfortunately, this leads to a disproportionately high number of Monte Carlo samples to be evaluated to ensure an estimation with high confidence for small probabilities. Thus, in this paper, we present a new Monte Carlo simulation method enhanced by a convolutional neural network. The sample-set used for this Monte Carlo approach is provided by artificially generating site-dependent ground motion time histories using a non-linear Kanai-Tajimi filter. Compared to several state-of-the-art studies, the convolutional neural network learns to extract the relevant input features and the structural response behavior autonomously from the entire time histories instead of learning from a set of hand-chosen intensity inputs. Training the neural network based on a chosen input sample set develops a meta-model that is then used as a meta-model to predict the response of the total Monte Carlo sample set. This paper presents two convolutional neural network-enhanced strategies that allow for a practical design approach of ground motion excited structures. The first strategy enables for an accurate response prediction around the mean of the distribution. It is, therefore, useful regarding structural serviceability. The second strategy enables for an accurate prediction around the tail end of the distribution. It is, therefore, beneficial for the prediction of the probability of failure.

Intelligent stiffness computation for plate and beam structures by neural network enhanced finite element analysis

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“…Heider et al 9 proposed an informed graph based neural network to investigate frame invariance in anisotropic elastoplastic materials. A Monte Carlo strategy was also developed 10,11 to evaluate the response statistics of nonlinear structural dynamics using FFNN and convolutional neural networks (CNNs). Similarly RNNs were used to efficiently predict non‐linear hysteric behavior of a structure subjected to random load history 12 .…”

A machine learning regression approach for predicting the bearing capacity of a strip footing on rock mass under inclined and eccentric load

“…These things can be reduced the calculation time for numerical modelling and selecting the impact parameters of practitioners. Fortunately, together with the development of artificial intelligence, machine learning is applied in data analysis in many scientific fields, including geotechnical problems, which have significant issues in calculating data (e.g., Fernández-Cabán et al, 2018;Ghahramani et al, 2020;Bamer et al, 2021;Wu and Snaiki, 2022). Some machine learning methods, which can be considered as the successful models in geotechnical problems, are artificial neural networks ~ANN, extreme learning machines ~ELM, support vector regression ~SVR, Gaussian process regression ~GPR, and stochastic gradient boosting trees ~SGBT (e.g., Yuan et al, 2021;Keawsawasvong et al, 2022c).…”

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“…However, this method lacks accuracy if the neural network is not provided with sufficient amount of data. Extending the training data set of the neural network has enabled the approach to also accurately predict the response in regions with low probability [7][8][9]. Another solution to speed up the estimation of low failure probabilities is to reduce the variance [10,11] and minimize the number of samples used in the Monte Carlo simulation, e.g., by subset simulations.…”