The study of the impact of random parameters on the load-carrying capacity of imperfect cylindrical stiffened shells remains limited, due to the expensive cost of experimental testing. In this study, a post-buckling analysis model to numerically determine the collapsed load is first introduced. However, it is challenging to analyze the probability characteristics of a shell considering multiple random parameters. Thus, in this paper, the direct probability integral method (DPIM), as a novel stochastic analysis method, is extended to address this issue. Given the lack of enough quantity of statistics about uncertainty factors, a back-propagation neural network improved by particle swarm optimization (BPNN-PSO) model for predicting the collapse load is established. Building upon this, a novel neural network-based DPIM is proposed. In the numerical example, we compare the calculated results with those using the analytical solution, path integral method, and Monte Carlo simulation, demonstrating the high accuracy and efficiency of DPIM. Finally, an efficient physical-based uncertainty quantification of imperfect stiffened shells is implemented by BPNN-PSO-based DPIM. The results reveal the effects caused by different random parameters on the load-carrying of imperfect cylindrical stiffened shells. In particular, the change in stiffened height will bring a huge reduction in structural reliability.

中文翻译：

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基于神经网络的 DPIM 用于具有多个随机参数的不完美圆柱加筋壳的不确定性量化


由于实验测试成本昂贵，随机参数对不完美圆柱加筋壳承载能力影响的研究仍然有限。在本研究中，首先引入了一种用于数值确定塌陷载荷的后屈曲分析模型。然而，考虑多个随机参数来分析壳的概率​​特征是具有挑战性的。因此，本文扩展了直接概率积分法（DPIM）作为一种新颖的随机分析方法来解决这个问题。鉴于缺乏足够数量的不确定性因素统计数据，建立了粒子群优化改进的反向传播神经网络（BPNN-PSO）模型来预测倒塌荷载。在此基础上，提出了一种新颖的基于神经网络的 DPIM。在数值算例中，我们将计算结果与解析解、路径积分法和蒙特卡罗模拟的计算结果进行了比较，证明了DPIM的高精度和高效性。最后，基于 BPNN-PSO 的 DPIM 实现了对不完美加筋壳的有效的基于物理的不确定性量化。结果揭示了不同随机参数对不完美圆柱加筋壳承载的影响。特别是刚度高度的变化会带来结构可靠性的巨大降低。