The response of an engineering structure is influenced by many variables, making it necessary to calculate and forecast the likelihood of limit state violations. This evaluation is crucial in assessing the safety of a structure in the presence of uncertainties that may have negative impacts. Several methods have been developed to assess the reliability of a structure, including Monte Carlo Simulation (MCS), First-order Reliability Method (FORM), and Kriging. However, these methods face a challenge in the face of high-dimensionality. This research proposes a unified framework: Dimension-reduction Reliability Analysis (DRRA) that uses a dimensionality-reduction method in the form of neural network to reduce the dimensionality of input variables before Active-learning reliability method combining Kriging and Monte Carlo Simulation (AK-MCS) is utilized to assess the reliability of the structure. The dimensionality-reduction method involves training an autoencoder and a deep feedforward network to compress the high-dimension training samples into a low-dimensional latent space. AK-MCS is then used to assess the reliability of the system in the latent space. To demonstrate the effectiveness of the proposed framework, a mathematical case study and two practical high-dimensional case studies are conducted. The results indicate that the DRRA framework achieves higher accuracy compared to previous studies, with a 0.92% improvement in the mathematical case study. However, in terms of efficiency, the DRRA framework is 12.61% less efficient in the same case study. In the practical higher-dimensional case study, the DRRA framework demonstrates a 0.15% increase in accuracy and a 5.52% improvement in efficiency compared to the previous study.

The response of an engineering structure is influenced by many variables, making it necessary to calculate and forecast the likelihood of limit state violations. This evaluation is crucial in assessing the safety of a structure in the presence of uncertainties that may have negative impacts. Several methods have been developed to assess the reliability of a structure, including Monte Carlo Simulation (MCS), First-order Reliability Method (FORM), and Kriging. However, these methods face a challenge in the face of high-dimensionality. This research proposes a unified framework: Dimension-reduction Reliability Analysis (DRRA) that uses a dimensionality-reduction method in the form of neural network to reduce the dimensionality of input variables before Active-learning reliability method combining Kriging and Monte Carlo Simulation (AK-MCS) is utilized to assess the reliability of the structure. The dimensionality-reduction method involves training an autoencoder and a deep feedforward network to compress the high-dimension training samples into a low-dimensional latent space. AK-MCS is then used to assess the reliability of the system in the latent space. To demonstrate the effectiveness of the proposed framework, a mathematical case study and two practical high-dimensional case studies are conducted. The results indicate that the DRRA framework achieves higher accuracy compared to previous studies, with a 0.92% improvement in the mathematical case study. However, in terms of efficiency, the DRRA framework is 12.61% less efficient in the same case study. In the practical higher-dimensional case study, the DRRA framework demonstrates a 0.15% increase in accuracy and a 5.52% improvement in efficiency compared to the previous study.

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