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This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To simultaneously handle these two types of time-varying features, a two-step approach is proposed: multiple change point locations are first identified on the basis of comparing the difference between the localized averages on sample covariance matrices, and then graph supports are recovered on the basis of a kernelized time-varying constrained L 1 -minimization for inverse matrix estimation (CLIME) estimator on each segment. We derive the rates of convergence for estimating the change points and precision matrices under mild moment and dependence conditions. In particular, we show that this two-step approach is consistent in estimating the change points and the piecewise smooth precision matrix function, under a certain high-dimensional scaling limit. The method is applied to the analysis of network structure of the S&P 500 index between 2003 and 2008.
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Physics-Constrained Dictionary Learning for Selective Laser Melting Process Monitoring
Compressed sensing (CS) as a new data acquisition technique has been applied to monitor manufacturing processes. With a few measurements, sparse coefficient vectors can be recovered by solving an inverse problem and original signals can be reconstructed. Dictionary learning methods have been developed and applied in combination with CS to improve the sparsity level of the recovered coefficient vectors. In this work, a physics-constrained dictionary learning approach is proposed to solve both of reconstruction and classification problems by optimizing measurement, basis, and classification matrices simultaneously with the considerations of the application-specific restrictions. It is applied in image acquisitions in selective laser melting (SLM). The proposed approach includes the optimization in two steps. In the first stage, with the basis matrix fixed, the measurement matrix is optimized by determining the pixel locations for sampling in each image. The optimized measurement matrix only includes one non-zero entry in each row. The optimization of pixel locations is solved based on a constrained FrameSense algorithm. In the second stage, with the measurement matrix fixed, the basis and classification matrices are optimized based on the K-SVD algorithm. With the optimized basis matrix, the coefficient vector can be recovered with CS. The original signal can be reconstructed by the linear combination of the basis matrix and the recovered coefficient vector. The original signal can also be classified to identify different machine states by the linear combination of the classification matrix and the coefficient vector.
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- Award ID(s):
- 1663227
- PAR ID:
- 10282303
- Date Published:
- Journal Name:
- Proceedings of 2021 IISE Annual Conference & Expo
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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