It is a famous result of Kempe that a lillkage can be designed togenerate any given plane algebraic curve. In this paper, Kempe's result is improvedto give a precise algorithm for generating Kempe linkage. We prov...It is a famous result of Kempe that a lillkage can be designed togenerate any given plane algebraic curve. In this paper, Kempe's result is improvedto give a precise algorithm for generating Kempe linkage. We proved that for analgebraic plane curve of degree n, Kempe linkage uses at most O(n4) links. Effortsto implement a program which may generate Kempe linkage and simulation of thegeneration process of the plane curves are presellted in the paper.展开更多
Abnormal conditions are hazardous in complex process systems, and the aim of condition recognition is to detect abnormal conditions and thus avoid severe accidents. The relationship of linkage fluctuation between moni...Abnormal conditions are hazardous in complex process systems, and the aim of condition recognition is to detect abnormal conditions and thus avoid severe accidents. The relationship of linkage fluctuation between monitoring variables can characterize the operation state of the system. In this study,we present a straightforward and fast computational method, the multivariable linkage coarse graining(MLCG) algorithm, which converts the linkage fluctuation relationship of multivariate time series into a directed and weighted complex network. The directed and weighted complex network thus constructed inherits several properties of the series in its structure. Thereby, periodic series convert into regular networks, and random series convert into random networks. Moreover, chaotic time series convert into scale-free networks. It demonstrates that the MLCG algorithm permits us to distinguish, identify, and describe in detail various time series. Finally, we apply the MLCG algorithm to practical observations series, the monitoring time series from a compressor unit, and identify its dynamic characteristics. Empirical results demonstrate that the MLCG algorithm is suitable for analyzing the multivariable linkage fluctuation relationship in complex electromechanical system. This method can be used to detect specific or abnormal operation condition, which is relevant to condition identification and information quality control of complex electromechanical system in the process industry.展开更多
文摘It is a famous result of Kempe that a lillkage can be designed togenerate any given plane algebraic curve. In this paper, Kempe's result is improvedto give a precise algorithm for generating Kempe linkage. We proved that for analgebraic plane curve of degree n, Kempe linkage uses at most O(n4) links. Effortsto implement a program which may generate Kempe linkage and simulation of thegeneration process of the plane curves are presellted in the paper.
基金supported by the National Natural Science Foundation of China(Grant No.51375375)
文摘Abnormal conditions are hazardous in complex process systems, and the aim of condition recognition is to detect abnormal conditions and thus avoid severe accidents. The relationship of linkage fluctuation between monitoring variables can characterize the operation state of the system. In this study,we present a straightforward and fast computational method, the multivariable linkage coarse graining(MLCG) algorithm, which converts the linkage fluctuation relationship of multivariate time series into a directed and weighted complex network. The directed and weighted complex network thus constructed inherits several properties of the series in its structure. Thereby, periodic series convert into regular networks, and random series convert into random networks. Moreover, chaotic time series convert into scale-free networks. It demonstrates that the MLCG algorithm permits us to distinguish, identify, and describe in detail various time series. Finally, we apply the MLCG algorithm to practical observations series, the monitoring time series from a compressor unit, and identify its dynamic characteristics. Empirical results demonstrate that the MLCG algorithm is suitable for analyzing the multivariable linkage fluctuation relationship in complex electromechanical system. This method can be used to detect specific or abnormal operation condition, which is relevant to condition identification and information quality control of complex electromechanical system in the process industry.
