Least-squares solution of AXB = D with respect to symmetric positive semidefinite matrix X is considered. By making use of the generalized singular value decomposition, we derive general analytic formulas, and present...Least-squares solution of AXB = D with respect to symmetric positive semidefinite matrix X is considered. By making use of the generalized singular value decomposition, we derive general analytic formulas, and present necessary and sufficient conditions for guaranteeing the existence of the solution. By applying MATLAB 5.2, we give some numerical examples to show the feasibility and accuracy of this construction technique in the finite precision arithmetic.展开更多
Currently, due to the detrimental effects on surface finish and machining system, chatter has been one crucial factor restricting robotic drilling operations, which improve both quality and efficiency of aviation manu...Currently, due to the detrimental effects on surface finish and machining system, chatter has been one crucial factor restricting robotic drilling operations, which improve both quality and efficiency of aviation manufacturing. Based on the matrix notch filter and fast wavelet packet decomposition, this paper presents a novel pre-generated matrix-based real-time chatter monitoring method for robotic drilling. Taking vibration characteristics of robotic drilling into account, the matrix notch filter is designed to eliminate the interference of spindle-related components on the measured vibration signal. Then, the fast wavelet packet decomposition is presented to decompose the filtered signal into several equidistant frequency bands, and the energy of each sub-band is obtained. Finally, the energy entropy which characterizes inhomogeneity of energy distribution is utilized as the feature to recognize chatter on-line, and the effectiveness of the presented algorithm is validated by extensive experimental data. The results show that the proposed algorithm can effectively detect chatter before it is fully developed. Moreover, since both filtering and decomposition of signal are implemented by the pre-generated matrices, calculation for an energy entropy of vibration signal with 512 samples takes only about 0.690 ms. Consequently, the proposed method achieves real-time chatter monitoring for robotic drilling, which is essential for subsequent chatter suppression.展开更多
Knowledge graph embedding, which maps the entities and relations into low-dimensional vector spaces, has demonstrated its effectiveness in many tasks such as link prediction and relation extraction. Typical methods in...Knowledge graph embedding, which maps the entities and relations into low-dimensional vector spaces, has demonstrated its effectiveness in many tasks such as link prediction and relation extraction. Typical methods include TransE, TransH, and TransR. All these methods map different relations into the vector space separately and the intrinsic correlations of these relations are ignored. It is obvious that there exist some correlations among relations because different relations may connect to a common entity. For example, the triples （Steve Jobs, PlaceOfBrith, California） and （Apple Inc., Location, California） share the same entity California as their tail entity. We analyze the embedded relation matrices learned by TransE/TransH/TransR, and find that the correlations of relations do exist and they are showed as low-rank structure over the embedded relation matrix. It is natural to ask whether we can leverage these correlations to learn better embeddings for the entities and relations in a knowledge graph. In this paper, we propose to learn the embedded relation matrix by decomposing it as a product of two low-dimensional matrices, for characterizing the low-rank structure. The proposed method, called TransCoRe （Translation-Based Method via Modeling the Correlations of Relations）, learns the embeddings of entities and relations with translation-based framework. Experimental results based on the benchmark datasets of WordNet and Freebase demonstrate that our method outperforms the typical baselines on link prediction and triple classification tasks.展开更多
A noise-reduction method with sliding called the local f-x Cadzow noise-reduction method, windows in the frequency-space （f-x） domain, is presented in this paper. This method is based on the assumption that the sign...A noise-reduction method with sliding called the local f-x Cadzow noise-reduction method, windows in the frequency-space （f-x） domain, is presented in this paper. This method is based on the assumption that the signal in each window is linearly predictable in the spatial direction while the random noise is not. For each Toeplitz matrix constructed by constant frequency slice, a singular value decomposition （SVD） is applied to separate signal from noise. To avoid edge artifacts caused by zero percent overlap between windows and to remove more noise, an appropriate overlap is adopted. Besides flat and dipping events, this method can enhance curved and conflicting events. However, it is not suitable for seismic data that contains big spikes or null traces. It is also compared with the SVD, f-x deconvolution, and Cadzow method without windows. The comparison results show that the local Cadzow method performs well in removing random noise and preserving signal. In addition, a real data example proves that it is a potential noise-reduction technique for seismic data obtained in areas of complex formations.展开更多
基金Subsidized by The Special Funds For Major State Basic Research Project G1999032803.
文摘Least-squares solution of AXB = D with respect to symmetric positive semidefinite matrix X is considered. By making use of the generalized singular value decomposition, we derive general analytic formulas, and present necessary and sufficient conditions for guaranteeing the existence of the solution. By applying MATLAB 5.2, we give some numerical examples to show the feasibility and accuracy of this construction technique in the finite precision arithmetic.
基金supported by the National Key R&D Program of China (No. 2017YFB1302601 and 2018YFB1702503)
文摘Currently, due to the detrimental effects on surface finish and machining system, chatter has been one crucial factor restricting robotic drilling operations, which improve both quality and efficiency of aviation manufacturing. Based on the matrix notch filter and fast wavelet packet decomposition, this paper presents a novel pre-generated matrix-based real-time chatter monitoring method for robotic drilling. Taking vibration characteristics of robotic drilling into account, the matrix notch filter is designed to eliminate the interference of spindle-related components on the measured vibration signal. Then, the fast wavelet packet decomposition is presented to decompose the filtered signal into several equidistant frequency bands, and the energy of each sub-band is obtained. Finally, the energy entropy which characterizes inhomogeneity of energy distribution is utilized as the feature to recognize chatter on-line, and the effectiveness of the presented algorithm is validated by extensive experimental data. The results show that the proposed algorithm can effectively detect chatter before it is fully developed. Moreover, since both filtering and decomposition of signal are implemented by the pre-generated matrices, calculation for an energy entropy of vibration signal with 512 samples takes only about 0.690 ms. Consequently, the proposed method achieves real-time chatter monitoring for robotic drilling, which is essential for subsequent chatter suppression.
基金This work was supported by the National Basic Research 973 Program of China under Grant No. 2014CB340405, the National Key Research and Development Program of China under Grant No. 2016YFB1000902, and the National Natural Science Foundation of China under Grant Nos. 61402442, 61272177, 61173008, 61232010, 61303244, 61572469, 91646120 and 61572473.
文摘Knowledge graph embedding, which maps the entities and relations into low-dimensional vector spaces, has demonstrated its effectiveness in many tasks such as link prediction and relation extraction. Typical methods include TransE, TransH, and TransR. All these methods map different relations into the vector space separately and the intrinsic correlations of these relations are ignored. It is obvious that there exist some correlations among relations because different relations may connect to a common entity. For example, the triples （Steve Jobs, PlaceOfBrith, California） and （Apple Inc., Location, California） share the same entity California as their tail entity. We analyze the embedded relation matrices learned by TransE/TransH/TransR, and find that the correlations of relations do exist and they are showed as low-rank structure over the embedded relation matrix. It is natural to ask whether we can leverage these correlations to learn better embeddings for the entities and relations in a knowledge graph. In this paper, we propose to learn the embedded relation matrix by decomposing it as a product of two low-dimensional matrices, for characterizing the low-rank structure. The proposed method, called TransCoRe （Translation-Based Method via Modeling the Correlations of Relations）, learns the embeddings of entities and relations with translation-based framework. Experimental results based on the benchmark datasets of WordNet and Freebase demonstrate that our method outperforms the typical baselines on link prediction and triple classification tasks.
基金support from the National Key Basic Research Development Program(Grant No.2007CB209600)National Major Science and Technology Program(Grant No.2008ZX05010-002)
文摘A noise-reduction method with sliding called the local f-x Cadzow noise-reduction method, windows in the frequency-space （f-x） domain, is presented in this paper. This method is based on the assumption that the signal in each window is linearly predictable in the spatial direction while the random noise is not. For each Toeplitz matrix constructed by constant frequency slice, a singular value decomposition （SVD） is applied to separate signal from noise. To avoid edge artifacts caused by zero percent overlap between windows and to remove more noise, an appropriate overlap is adopted. Besides flat and dipping events, this method can enhance curved and conflicting events. However, it is not suitable for seismic data that contains big spikes or null traces. It is also compared with the SVD, f-x deconvolution, and Cadzow method without windows. The comparison results show that the local Cadzow method performs well in removing random noise and preserving signal. In addition, a real data example proves that it is a potential noise-reduction technique for seismic data obtained in areas of complex formations.
