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Features of jumping loads are essentially high-dimensional random variables but have been simplistically modeled owing to the lack of proper mathematical tools. Generative adversarial networks (GANs) in conjunction with deep learning technology are adopted herein for modeling the jumping loads. Conditional GANs (CGANs) combined with Wasserstein GANs (WGANs) with gradient penalty (WGANs-GP) are adopted in the impulse modeling, where a multi-layer perceptron and a convolutional neural network are employed for the discriminator and generator, respectively. As for the impulse amplitude sequence and interval sequence modeling, similar CGANs combined with WGANs-GP are adopted, where recurrent neural networks are employed for both the generator and discriminator. A large amount of measured individual jumping loads are utilized in training GANs to ensure the generated samples can simulate the real ones well. After training, the individual jumping loads are simulated by connecting the generated impulse samples, based on the generated impulse amplitude sequence samples and interval sequence samples. The simulated jumping loads can be used to assess the vibration performance of assembly structures, such as grandstands, concert halls, and gym floors. Moreover, the established GANs can be extended to the modeling of other stochastic dynamic excitations. [ABSTRACT FROM AUTHOR]

Severe vibrations may occur on slender structures like footbridges and cantilever stands due to human-induced loads such as walking, jumping or bouncing. Currently, to develop a load model for structural design, the main features, such as periodicity and stationarity of experimental load records, are artificially extracted and then mathematically modeled. Different physical features have been included in different load models, i.e. no unified load model exists for different individual activities. The recently emerged generative adversarial networks can be used to model high-dimensional random variables. The probability distribution of these variables learned from real samples can be used to generate new samples, avoiding extracting features artificially. In this paper, a new model is proposed which combines the conditional generative adversarial networks and Wasserstein generative adversarial networks with gradient penalty to generate individual walking, jumping and bouncing loads. The generator of the model has five fully connected layers and a one-dimensional convolutional layer, and the discriminator has five fully connected layers. After one million training steps using the experimental records, the generator can generate high-quality samples similar to real samples in waveform. Finally, by comparing the power spectral densities and single degree of freedom system's responses of the generated samples with real samples, it is further proved that the proposed generative adversarial network model can be used to simulate various human-induced loads. Source code of the model along with its trained weights is provided to the readers to further analysis and application. [ABSTRACT FROM AUTHOR]

Modern slender structures such as long-span floors and cantilever stands are sensitive to jumping-induced vibrations. A conventional deterministic Fourier series model for the human jumping load may overestimate a structure's responses in resonance condition. This paper suggests a power spectral density (PSD) function for the individual jumping load, which was treated as a narrowband stationary stochastic process. Experiments were conducted on individual jumping loads resulting in 334 records from 73 subjects. Statistical analysis of the records led to experimental PSD curves on which a symmetrical bilinear function was suggested. The proposed PSD function is centered on the given jumping frequency and its integer multiples. The function's parameters were determined by equating the total energy of the proposed PSD with that of the experimental PSD. Application of the proposed PSD for predicting a floor's peak response via the stochastic vibration theory was then presented. The predictions for an experimental floor model subjected to individual jumping were compared with the measured peak responses. The comparisons demonstrated that the proposed PSD function was applicable for predicting the floor's response to individual jumping. Finally, the framework for calculating crowd-induced structure vibrations using the suggested PSD was also discussed. [ABSTRACT FROM AUTHOR]