In structural reliability analysis, the estimation of extremely small failure probability with high-dimensional inputs remains a highly challenging computational problem. In this paper, a recently proposed surrogate model for high-dimensional approximation—the anisotropic Radial Basis Function (RBF) model embedded with Multiscale Graph Correlation (MGC-ARBF)—and an importance sampling method—the cross-entropy importance sampling with failure-informed dimension reduction (iCEred)—are introduced and closely integrated. The iCEred method exploits prediction information from MGC-ARBF to perform failure-informed dimension reduction (FDR) and generate importance samples. The MGC-ARBF model actively selects informative training points based on its own needs. However, FDR requires the computation of the gradient covariance matrix, which will be very time-consuming when using traditional difference methods. To address this, we first derive the adjoint gradient of MGC-ARBF within the framework of Jackknife resampling and provide matrix-operation methods for the computation of adjoint gradients at numerous importance samples. This substantially reduces the computational cost associated with FDR. Four numerical examples and one engineering problem are presented to demonstrate the performance of the proposed method. Compared with state-of-the-art methods, the proposed method demonstrates strong competitiveness in minimizing the number of function evaluations, while maintaining acceptable computational time.
We investigate the shape sensitivity of functionals arising in inverse problems involving distributed optical fiber sensors for structural health monitoring and material parameter identification. These sensors are deployed along curves, leading to objective functionals whose integrands depend not only on spatial position but also on the local tangent direction of the sensing path, which prevents a direct application of classical shape-calculus tools. To address this issue, we develop a shape-derivative framework that explicitly accounts for this tangent dependence, enabling gradient-based, non-parametric shape optimization of sensor geometries. In particular, we derive shape derivatives of T- and D-optimality criteria associated with the Fisher information matrix, as well as their counterparts based on the modified constitutive relation error. The resulting expressions extend classical Hadamard formulas and provide a rigorous basis for continuous, gradient-driven optimization of distributed sensor paths, allowing efficient and systematic sensor placement without relying on predefined geometric parameterizations.
The preliminary design of autonomous underwater gliders (AUGs) is intrinsically challenging due to the strong coupling between the external hydrodynamic shape, the hydrostatic balance, the structural integrity, and internal packaging constraints. This complexity is further amplified for bio-inspired configurations, whose rich geometric parametrizations lead to high-dimensional design spaces that are difficult to explore using conventional optimization approaches. This work presents a machine learning enabled bi-level multidisciplinary design optimization (MDO) framework for the performance-driven design of a manta-ray-inspired AUG. At the upper level, hydrodynamically efficient external geometries are explored in a reduced design space obtained through physics-driven parametric model embedding, which identifies a low-dimensional latent representation directly correlated with the lift, drag, and pressure distributions. At the lower level, a constrained internal sizing problem determines the minimum feasible empty weight by accounting for structural, hydrostatic, geometric, and payload constraints. To render the resulting bi-level problem computationally tractable, a multi-fidelity surrogate-based optimization strategy is adopted, combining low- and high-fidelity hydrodynamic models with stochastic radial basis function surrogates and adaptive Bayesian sampling. The framework enables efficient exploration of the coupled design space while rigorously managing model uncertainty and computational cost. The optimized configurations exhibit a 14.7
This study presents a topology optimization framework for dual-phase-change material (dual-PCM) heat sinks under time-varying thermal loads, with temperature oscillation suppression as the primary objective. The framework is developed based on the FEniTop platform and extended to transient nonlinear heat conduction with phase change. A degraded discrete material optimization (DMO) interpolation scheme is adopted to handle the distribution of a high-conductivity material (HCM), a low-melting-point alloy (LMPA), and a conventional PCM in a unified manner while ensuring clear material separation. The method is first applied to two-dimensional benchmark problems to quantify the benefit of introducing LMPA. Compared with the HCM-PCM configuration, the addition of 10
This paper presents pyTOM, an open-source topology optimization (TO) framework developed for the design of magnetic actuators. The framework integrates magnetostatic vector potential formulations with a density-based TO scheme incorporating Helmholtz filtering, Heaviside projection, and SIMP interpolation of magnetic reluctivity. Magnetic forces are computed via the Maxwell stress tensor, and the design variables are updated using the Method of Moving Asymptotes. The framework addresses three distinctive characteristics of TO for electromechanical devices within a unified computational environment. First, both permanent magnets and coil excitations are modeled as field sources. Second, nonlinear magnetic behavior due to saturation effect is captured through a field-dependent reluctivity model solved via a Newton–Raphson scheme. Third, a multi-position analysis is introduced to evaluate actuator performance across multiple plunger positions. Several numerical examples demonstrate the accuracy and capability of the proposed framework. The accuracy of the magnetic field computation is first validated against COMSOL in an interior permanent magnet motor benchmark. Comparative studies between linear and nonlinear material models then illustrate the effect of magnetic saturation on the design result. Finally, TO results obtained under multiple plunger positions are presented and discussed. The pyTOM framework is intended to serve as an accessible educational platform for TO in electromechanical devices, including electric motors and actuators.
