Non-probabilistic convex models are powerful tools for structural model updating with uncertain‑but-bounded parameters. However, existing non-probabilistic model updating (NPMU) methods often struggle with detecting parameter correlation due to limited prior information. Worth still, the unique core steps of NPMU, involving nested inner layer forward uncertainty propagation and outer layer inverse parameter updating, present challenges in efficiency and convergence. In response to these challenges, a novel and flexible NPMU scheme is introduced, integrating analytical correlation propagation and parallel interval bounds prediction to enable automatic detection of parameter correlations. In the forward uncertainty propagation phase, a linear coordinate transformation is applied to map the original parameter space to a standard hypercube space, simplifying correlation-involved bounds prediction into conventional interval bounds prediction. Moreover, an analytical correlation propagation formula is derived using a second-order response approximation to sidestep the complexities of geometry-based correlation calculations. To expedite forward propagation, a derivative-aware neural network model is employed to replace the physical solver, facilitating improved fitting capabilities and automatic differentiation, including the calculation of Jacobian and Hessian matrices essential for correlation propagation. The neural network's inherent parallelism accelerates interval bounds prediction through parallel computation of samples. In the inverse parameter updating phase, the block coordinate descent algorithm is embraced to narrow the search space and boost convergence capabilities, while the perturbation method is utilized to determine the optimal starting point for optimization. Two numerical examples illustrate the efficacy of the proposed method in updating structural models while considering correlations.

中文翻译：

---

基于分析相关传播公式和导数感知深度神经网络元模型的高效非概率并行模型更新


非概率凸模型是使用不确定但有界参数更新结构模型的强大工具。然而，由于先验信息有限，现有的非概率模型更新 （NPMU） 方法经常难以检测参数相关性。值得一提的是，NPMU 独特的核心步骤，包括嵌套的内层前向不确定性传播和外层逆参数更新，在效率和收敛性方面提出了挑战。为了应对这些挑战，引入了一种新颖灵活的 NPMU 方案，该方案集成了分析相关性传播和并行区间边界预测，以实现参数相关性的自动检测。在前向不确定性传播阶段，应用线性坐标变换将原始参数空间映射到标准超立方体空间，将涉及相关性的边界预测简化为常规的区间边界预测。此外，使用二阶响应近似推导出解析相关传播公式，以回避基于几何的相关计算的复杂性。为了加快前向传播，采用导数感知神经网络模型来取代物理求解器，从而促进改进的拟合能力和自动微分，包括计算对相关性传播至关重要的雅可比矩阵和 Hessian 矩阵。神经网络固有的并行性通过样本的并行计算加速区间边界预测。在逆参数更新阶段，采用块坐标下降算法来缩小搜索空间并提高收敛能力，同时利用扰动方法来确定优化的最佳起点。 两个数值示例说明了所提出的方法在考虑相关性的同时更新结构模型的有效性。