Probabilistic evaluation of seismic responses using deep learning method

Abstract

Structural failures caused by a strong earthquake may induce a large number of casualties and huge socioeconomic losses. To design a structure that can withstand such earthquake events, it is essential to accurately estimate the nonlinear structural responses caused by strong ground motions. As a replacement of an onerous and complex nonlinear time history analysis, simple regression-based equations have been widely adopted in routine engineering practices. It is, however, noted that the response prediction is deterministic, which cannot quantify the variabilities stemming from the nonlinear behavior of the structural system, i.e. varying seismic demands given the same earthquake intensity value. In addition, it is well known that the accuracy of prediction based on the regression-based equations is limited. In order to quantify such uncertainties and improve the prediction accuracy, this paper proposes a probabilistic deep neural network model based on a Bayesian deep learning method. By introducing a loss function which is proportional to the negative log likelihood of the Gaussian distribution function, the mean and variance of the structural responses can be obtained. This assessment is important especially for earthquake engineering applications because of large randomness in the input ground motion details and their significant impact on the structural responses. Moreover, using the proposed probabilistic deep neural network model, one can estimate seismic fragilities of the structural system efficiently. Thorough numerical investigations are carried out to demonstrate the proposed method. The supporting source code and data are available for download at http://ERD2.snu.ac.kr.