| Author: | Zhang, Yu |
| Title: | Adaptive kriging model for rare events estimation and rLSTM-assisted dynamic reliability analysis |
| Advisors: | Dong, You (CEE) Zhu, Songye (CEE) |
| Degree: | Ph.D. |
| Year: | 2025 |
| Subject: | Structural stability Reliability (Engineering) Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Civil and Environmental Engineering |
| Pages: | xxi, 223 pages : color illustrations |
| Language: | English |
| Abstract: | Uncertainties in structural materials and environmental conditions are widely recognized for their significant impact on structural performance. For instance, concrete strength is statistically determined from a limited number of specimens, and similar variability is observed in the modulus and yield strength of steel, both of which should be treated as random variables. In addition, natural variability is present in environmental conditions, such as wind velocity. As a result, structural responses are inherently uncertain due to the propagation of these uncertainties from both structural parameters and external loads. Therefore, it is essential to thoroughly investigate the uncertainty propagation process. Structural reliability analysis plays a crucial role in assessing structural safety and guiding the design process. However, efficiently and accurately estimating failure probabilities remains a significant challenge. Over the past few decades, various approaches have been developed to address this issue. Among them, Monte Carlo simulation (MCS) is the most straightforward method, but it demands substantial computational resources, particularly when dealing with time-intensive performance functions. Although the first- and second-order reliability methods are computationally efficient, they often lack accuracy when applied to nonlinear structures. Recently, surrogate model-based methods have garnered increasing attention. A surrogate model serves as an efficient alternative to the original costly physical model. Commonly used surrogate models include the Kriging model, polynomial chaos expansion, support vector regression, and neural networks. The adaptive Kriging model has gained popularity in recent years due to its ability to be refined iteratively using active learning strategies. However, improvements in its efficiency for estimating failure probabilities are still needed. Structural failures are typically rare events, and applying adaptive Kriging with MCS is inefficient for estimating small failure probabilities, as training the Kriging model with a large number of candidate samples is time-consuming. To address this challenge, a distance-based subdomain approach is developed to focus on candidate samples near the limit state surface. During training, the Kriging model is refined iteratively within these subdomains, rather than across the entire Monte Carlo population. To further reduce the computational cost of performance function evaluations, a new stopping criterion is proposed. This criterion accounts for the accuracy of failure probability estimation, allowing the active learning process to terminate at an appropriate stage. Furthermore, for estimating very rare events, such as failure probabilities smaller than 10-6, an adaptive Kriging model with spherical decomposition-based Monte Carlo simulation can be employed. However, conventional stopping criteria are inadequate for halting the active training process at an appropriate stage, especially for practical engineering structures. Therefore, a new stopping criterion tailored to the adaptive Kriging model with spherical decomposition-based Monte Carlo simulation is proposed, based on the relative error of failure probability. In addition, the reliability analysis of stochastic dynamic systems, such as engineering structures subjected to stochastic seismic excitation or wind loads, remains challenging. Existing studies primarily focus on extreme value theory and the moments method. The first passage failure probability can be estimated from the extreme value distribution of the responses of interest. However, constructing surrogate models for stochastic dynamic systems is difficult due to the high dimensionality that arises when simulating stochastic excitations. For example, the spectral representation method requires thousands of random phases to simulate the stochastic excitation. Even when only the extreme response is of concern, the Kriging model is unsuitable for metamodeling due to the curse of dimensionality. To enable the adaptive Kriging model for the reliability analysis of stochastic dynamic systems, a novel long short-term memory network (rLSTM) is proposed. This network considers both time-series stochastic excitation and random structural parameters to predict time history responses. The rLSTM is integrated with an autoencoder to identify low-dimensional latent variables for representing the approximate extreme value space created by the rLSTM, which are then used to construct the Kriging model. An active learning strategy is subsequently employed to facilitate the reliability analysis of stochastic dynamic systems. To improve the accuracy and training stability of rLSTM network, a physics-informed rLSTM is constructed by incorporating the uncertain governing equations of dynamics. Additionally, conventional adaptive Kriging model continuously require information from the performance function, making parallel computing infeasible. This limitation significantly impedes the application of the adaptive Kriging model to computationally expensive models. To tackle this problem, a prediction error-based offline learning strategy is introduced. This approach allows the adaptive Kriging model to be refined in a single step, significantly reducing the computational burden of reliability analysis for stochastic dynamic systems. Overall, this research put emphasis on adaptive Kriging model for rare events estimation and reliability analysis of stochastic dynamic systems. The sampling scheme and stopping criteria are improved for small failure probabilities estimation. With the aid of long short-term memory networks, latent variables for constructing Kriging model of extreme responses are identified, making the adaptive Kriging model available for reliability analysis of stochastic dynamic systems. |
| Rights: | All rights reserved |
| Access: | open access |
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