Many engineering design problems can be formulated as decisions between two possible options. This is the case, for example, when a quantity of interest must be maintained below or above some threshold. The threshold thereby determines which input parameters lead to which option, and creates a boundary between the two options known as the decision boundary. This report details a machine learning approach for estimating decision boundaries, based on support vector machines (SVMs), that is amenable to large scale computational simulations. Because it is computationally expensive to evaluate each training sample, the approach iteratively estimates the decision boundary in a manner that requires relatively few training samples to glean useful estimates. The approach is then demonstrated on three example problems from structural mechanics and heat transport.
The inverse methods team provides a set of tools for solving inverse problems in structural dynamics and thermal physics, and also sensor placement optimization via Optimal Experimental Design (OED). These methods are used for designing experiments, model calibration, and verfication/validation analysis of weapons systems. This document provides a user's guide to the input for the three apps that are supported for these methods. Details of input specifications, output options, and optimization parameters are included.
This paper presents a topology optimization formulation for frequency-domain dynamics to reduce solution dependence upon initial guess and considered loading conditions. Due to resonance phenomena in undamped steady-state dynamics, objectives measuring dynamic response possess many local minima that may represent poor solutions to a design problem, an issue exacerbated for design with respect to multiple frequencies. We propose an extension of the modified error-in-constitutive-equations (MECE) method, used previously in material identification inverse problems, as a new approach for frequency-domain dynamics topology optimization to mitigate these issues. The main idea of the proposed framework is to incorporate an additional penalty-like term in the objective function that measures the discrepancy in the constitutive relations between stresses and strains and between inertial forces and displacements. Then, the design problem is cast within a PDE-constrained optimization formulation in which we seek displacements, stresses, inertial forces, and a density-field solution that minimize our new objective subject to conservation of linear momentum plus some additional constraints. We show that this approach yields superior designs to conventional gradient-based optimization approaches that solely use a functional of displacements as the objective, while strictly enforcing the constitutive equations. The MECE strategy integrates into a density-based topology optimization scheme for void–solid or two-phase material structural design. We highlight the merits of our approach in a variety of scenarios for direct frequency response design, considering multiple frequency load cases and structural objectives.
Barcellos, Debora R.; Coury, Francisco G.; Emery, Antoine; Sanders, Clay M.; Tong, Jianhua; McDaniel, Anthony H.; Wolverton, Christopher; O'Hayre, Ryan
Ruddlesden-Popper (layered perovskite) phases are attracting significant interest because of their unique potential for many applications requiring mixed ionic and electronic conductivity. Here we report a new, previously undiscovered layered perovskite of composition, CexSr2-xMnO4 (x = 0.1, 0.2, and 0.3). Furthermore, we demonstrate that this new system is suitable for solar thermochemical hydrogen production (STCH). Synchrotron radiation X-ray diffraction and transmission electron microscopy are performed to characterize this new system. Density functional theory calculations of phase stability and oxygen vacancy formation energy (1.76, 2.24, and 2.66 eV/O atom, respectively with increasing Ce content) reinforce the potential of this phase for STCH application. Experimental hydrogen production results show that this materials system produces 2-3 times more hydrogen than the benchmark STCH oxide ceria at a reduction temperature of 1400 °C and an oxidation temperature of 1000 °C.
This letter demonstrates the design of continuously graded elastic cylinders to achieve passive cloaking from harmonic acoustic excitation, both at single frequencies and over extended bandwidths. The constitutive parameters in a multilayered, constant-density cylinder are selected in a partial differential equation-constrained optimization problem, such that the residual between the pressure field from an unobstructed spreading wave in a fluid and the pressure field produced by the cylindrical inclusion is minimized. The radial variation in bulk modulus appears fundamental to the cloaking behavior, while the shear modulus distribution plays a secondary role. Such structures could be realized with functionally-graded elastic materials.
We use machine learning (ML) to infer stress and plastic flow rules using data from representative polycrystalline simulations. In particular, we use so-called deep (multilayer) neural networks (NN) to represent the two response functions. The ML process does not choose appropriate inputs or outputs, rather it is trained on selected inputs and output. Likewise, its discrimination of features is crucially connected to the chosen input-output map. Hence, we draw upon classical constitutive modeling to select inputs and enforce well-accepted symmetries and other properties. In the context of the results of numerous simulations, we discuss the design, stability and accuracy of constitutive NNs trained on typical experimental data. With these developments, we enable rapid model building in real-time with experiments, and guide data collection and feature discovery.