A Substructure Synthesis Method with Nonlinear ROM Including Geometric Nonlinearities

Large flexible aircraft are often accompanied by large deformations during flight leading to obvious geometric nonlinearities in response. Geometric nonlinear dynamic response simulations based on full-order models often carry unbearable computing burden. Meanwhile, geometric nonlinearities are caused by large flexible wings in most cases and the deformation of fuselages is small. Analyzing the whole aircraft as a nonlinear structure will greatly increase the analysis complexity and cost. The analysis of complicated aircraft structures can be more efficient and simplified if subcomponents can be divided and treated. This paper aims to develop a hybrid interface substructure synthesis method by expanding the nonlinear reduced-order model (ROM) with the implicit condensation and expansion (ICE) approach, to estimate the dynamic transient response for aircraft structures including geometric nonlinearities. A small number of linear modes are used to construct a nonlinear ROM for substructures with large deformation, and linear substructures with small deformation can also be assembled comprehensively. The method proposed is compatible with finite element method (FEM), allowing for realistic engineering model analysis. Numerical examples with large flexible aircraft models are calculated to validate the accuracy and efficiency of this method contrasted with nonlinear FEM.

Evaluation of POD based surrogate models of fields resulting from nonlinear FEM simulations

Surrogate modelling is a powerful tool to replace computationally expensive nonlinear numerical simulations, with fast representations thereof, for inverse analysis, model-based control or optimization. For some problems, it is required that the surrogate model describes a complete output field. To construct such surrogate models, proper orthogonal decomposition (POD) can be used to reduce the dimensionality of the output data. The accuracy of the surrogate models strongly depends on the (pre)processing actions that are used to prepare the data for the dimensionality reduction. In this work, POD-based surrogate models with Radial Basis Function interpolation are used to model high-dimensional FE data fields. The effect of (pre)processing methods on the accuracy of the result field is systematically investigated. Different existing methods for surrogate model construction are compared with a novel method. Special attention is given to data fields consisting of several physical meanings, e.g. displacement, strain and stress. A distinction is made between the errors due to truncation and due to interpolation of the data. It is found that scaling the data per physical part substantially increases the accuracy of the surrogate model.

Magnetostatic reciprocity for MR magnet design

Electromagnetic reciprocity has long been a staple in MR radio-frequency development, offering geometrical insights and a figure of merit for various resonator designs. In a similar manner, we use magnetostatic reciprocity to compute manufacturable solutions of complex magnet geometries, by establishing a quantitative metric for the placement and subsequent orientation of discrete pieces of permanent magnetic material. Based on magnetostatic theory and nonlinear FEM simulations, it is shown how assembled permanent magnet setups perform in the embodiment of a variety of designs, and how magnetostatic reciprocity is leveraged in the presence of difficulties associated with self-interactions, to fulfil various design objectives, including self-assembled micro magnets, adjustable magnetic arrays, and an unbounded magnetic field intensity in a small volume, despite realistic saturation field strengths.

A Pinning Actor-Critic Structure-Based Algorithm for Sizing Complex-Shaped Depth Profiles in MFL Inspection with High Degree of Freedom

One of the most efficient nondestructive methods for pipeline in-line inspection is magnetic flux leakage (MFL) inspection. Estimating the size of the defect from MFL signal is one of the key problems of MFL inspection. As the inspection signal is usually contaminated by noise, sizing the defect is an ill-posed inverse problem, especially when sizing the depth as a complex shape. An actor-critic structure-based algorithm is proposed in this paper for sizing complex depth profiles. By learning with more information from the depth profile without knowing the corresponding MFL signal, the algorithm proposed saves computational costs and is robust. A pinning strategy is embedded in the reconstruction process, which highly reduces the dimension of action space. The pinning actor-critic structure (PACS) helps to make the reward for critic network more efficient when reconstructing the depth profiles with high degrees of freedom. A nonlinear FEM model is used to test the effectiveness of algorithm proposed under 20 dB noise. The results show that the algorithm reconstructs the depth profile of defects with good accuracy and is robust against noise.