Stochastic differential equations(SDEs)are mathematical models that are widely used to describe complex processes or phenomena perturbed by random noise from different sources.The identification of SDEs governing a sy...Stochastic differential equations(SDEs)are mathematical models that are widely used to describe complex processes or phenomena perturbed by random noise from different sources.The identification of SDEs governing a system is often a challenge because of the inherent strong stochasticity of data and the complexity of the system’s dynamics.The practical utility of existing parametric approaches for identifying SDEs is usually limited by insufficient data resources.This study presents a novel framework for identifying SDEs by leveraging the sparse Bayesian learning(SBL)technique to search for a parsimonious,yet physically necessary representation from the space of candidate basis functions.More importantly,we use the analytical tractability of SBL to develop an efficient way to formulate the linear regression problem for the discovery of SDEs that requires considerably less time-series data.The effectiveness of the proposed framework is demonstrated using real data on stock and oil prices,bearing variation,and wind speed,as well as simulated data on well-known stochastic dynamical systems,including the generalized Wiener process and Langevin equation.This framework aims to assist specialists in extracting stochastic mathematical models from random phenomena in the natural sciences,economics,and engineering fields for analysis,prediction,and decision making.展开更多
In this paper, a stochastic model of plague is first studied by subspace identification. First, the discrete model of plague is obtained based on the classical model. The corresponding stochastic model is proposed for...In this paper, a stochastic model of plague is first studied by subspace identification. First, the discrete model of plague is obtained based on the classical model. The corresponding stochastic model is proposed for the existence of stochastic disturbances. Second, for the model, the parameter matrices and noise intensity are obtained. Finally, the simulations of the model show that the subspace identification is more precise than least square method.展开更多
In this paper, a data-driven stochastic subspace identification(SSI-DATA) technique is proposed as an advanced stochastic system identification(SSI) to extract the inter-area oscillation modes of a power system from w...In this paper, a data-driven stochastic subspace identification(SSI-DATA) technique is proposed as an advanced stochastic system identification(SSI) to extract the inter-area oscillation modes of a power system from wide-area measurements. For accurate and robust extraction of the modes’ parameters(frequency, damping and mode shape), SSI has already been verified as an effective identification algorithm for output-only modal analysis.The new feature of the proposed SSI-DATA applied to inter-area oscillation modal identification lies in its ability to select the eigenvalue automatically. The effectiveness of the proposed scheme has been fully studied and verified,first using transient stability data generated from the IEEE16-generator 5-area test system, and then using recorded data from an actual event using a Chinese wide-area measurement system(WAMS) in 2004. The results from the simulated and recorded measurements have validated the reliability and applicability of the SSI-DATA technique in power system low frequency oscillation analysis.展开更多
基金supported by the National Key Research and Development Program of China(2018YFB1701202)the National Natural Science Foundation of China(92167201 and 51975237)the Fundamental Research Funds for the Central Universities,Huazhong University of Science and Technology(2021JYCXJJ028)。
文摘Stochastic differential equations(SDEs)are mathematical models that are widely used to describe complex processes or phenomena perturbed by random noise from different sources.The identification of SDEs governing a system is often a challenge because of the inherent strong stochasticity of data and the complexity of the system’s dynamics.The practical utility of existing parametric approaches for identifying SDEs is usually limited by insufficient data resources.This study presents a novel framework for identifying SDEs by leveraging the sparse Bayesian learning(SBL)technique to search for a parsimonious,yet physically necessary representation from the space of candidate basis functions.More importantly,we use the analytical tractability of SBL to develop an efficient way to formulate the linear regression problem for the discovery of SDEs that requires considerably less time-series data.The effectiveness of the proposed framework is demonstrated using real data on stock and oil prices,bearing variation,and wind speed,as well as simulated data on well-known stochastic dynamical systems,including the generalized Wiener process and Langevin equation.This framework aims to assist specialists in extracting stochastic mathematical models from random phenomena in the natural sciences,economics,and engineering fields for analysis,prediction,and decision making.
基金Acknowledgments This work was supported by the National Natural Science Foundation of China （NSFC） under Grant 61374137 and the State Key Laboratory of Integrated Automation of Process Industry Technology and Research Center of National Metallurgical Automation Fundamental Research Funds （2013ZCX02-03）.
文摘In this paper, a stochastic model of plague is first studied by subspace identification. First, the discrete model of plague is obtained based on the classical model. The corresponding stochastic model is proposed for the existence of stochastic disturbances. Second, for the model, the parameter matrices and noise intensity are obtained. Finally, the simulations of the model show that the subspace identification is more precise than least square method.
基金supported by the National Natural Science Foundation of China(No.51507028)the Hong Kong Polytechnic University under Project G-UA3Z
文摘In this paper, a data-driven stochastic subspace identification(SSI-DATA) technique is proposed as an advanced stochastic system identification(SSI) to extract the inter-area oscillation modes of a power system from wide-area measurements. For accurate and robust extraction of the modes’ parameters(frequency, damping and mode shape), SSI has already been verified as an effective identification algorithm for output-only modal analysis.The new feature of the proposed SSI-DATA applied to inter-area oscillation modal identification lies in its ability to select the eigenvalue automatically. The effectiveness of the proposed scheme has been fully studied and verified,first using transient stability data generated from the IEEE16-generator 5-area test system, and then using recorded data from an actual event using a Chinese wide-area measurement system(WAMS) in 2004. The results from the simulated and recorded measurements have validated the reliability and applicability of the SSI-DATA technique in power system low frequency oscillation analysis.
