Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. This work introduces a novel approach called physics-informed neural network with sparse regression to discover governing partial differential equations from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this discovery approach seamlessly integrates the strengths of deep neural networks for rich representation learning, physics embedding, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the equations. The efficacy and robustness of this method are demonstrated, both numerically and experimentally, on discovering a variety of partial differential equation systems with different levels of data scarcity and noise accounting for different initial/boundary conditions. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.
It is widely recognized that as electronic systems’ operating frequency shifts to microwave and millimeter wave bands, the integration of ferrite passive devices with semiconductor solid state active devices holds significant advantages in improved miniaturization, bandwidth, speed, power and production costs, among others. Traditionally, ferrites have been employed in discrete bulk form, despite attempts to integrate ferrite as films within microwave integrated circuits. Technical barriers remain centric to the incompatibility between ferrite and semiconductor materials and their processing protocols. In this review, we present past and present efforts at ferrite integration with semiconductor platforms with the aim to identify the most promising paths to realizing the complete integration of on-chip ferrite and semiconductor devices, assemblies and systems.
Copper ferrite films have been deposited on ͑100͒ MgO substrates by pulsed-laser deposition. The oxygen pressure used in deposition was varied from 1 to 120 mTorr with the substrate temperature fixed at 700°C. Magnetization values are measured to increase with oxygen pressure, reaching a maximum value of 2480 G, which is a 42% increase over the bulk equilibrium value. Extended x-ray absorption spectroscopy shows that the Cu cation inversion ␦ ͓defined as ͑Cu 1−␦ Fe ␦ ͒ tet ͓Cu ␦ Fe 2−␦ ͔ oct O 4 ͔ decreases monotonically from 0.72 to 0.55 with increasing saturation magnetization.
Summary
Computational modeling, in addition to data analytics, plays an important role in structural health monitoring (SHM). The high‐fidelity computational model based on the design and construction information provide important dynamics information of the structure and, more importantly, can be updated against field measurements for SHM purposes such as damage detection, response prediction, and reliability assessment. In this paper, we present a unique skyscraper (Al‐Hamra Tower) located in Kuwait City and its high‐fidelity computational model using ETABS for structural health monitoring applications. The tower is made of cast‐in‐place reinforced concrete with a core of shear walls and two curved shear walls running the height of the building (approximately 413 m with 86 floors in total). Interesting static and dynamic characteristics of the tower are described. System identification, interferometry‐based wave propagation analysis, and wave‐based damage detection are performed using synthetic data. This work mainly presents the phase of numerical investigations, which serves as a basis for correlating the field monitoring data to the model of the building in future work.
Identifying damage of structural systems is typically characterized as an inverse problem which might be ill-conditioned due to aleatory and epistemic uncertainties induced by measurement noise and modeling error. Sparse representation can be used to perform inverse analysis for the case of sparse damage. In this article, we propose a novel two-stage sensitivity analysis–based framework for both model updating and sparse damage identification. Specifically, an [Formula: see text] Bayesian learning method is first developed for updating the intact model and uncertainty quantification so as to set forward a baseline for damage detection. A sparse representation pipeline built on a quasi-[Formula: see text] method, for example, sequential threshold least squares regression, is then presented for damage localization and quantification. In addition, Bayesian optimization together with cross-validation is developed to heuristically learn hyperparameters from data, which saves the computational cost of hyperparameter tuning and produces more reliable identification result. The proposed framework is verified by three examples, including a 10-story shear-type building, a complex truss structure, and a shake-table test of an eight-story steel frame. Results show that the proposed approach is capable of both localizing and quantifying structural damage with high accuracy.
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