Research On The Data-driven System Dynamics

In this dissertation,the dynamics of data-driven systems are investigated based on time series analysis.Characterization of plastical dynamics of high entropy alloys,design of the prediction schemes corresponding to the dynamical evolution of systems,analysis and prediction of the influenza-like illness in America,and exploration of the mathematical model by sparse dynamics from data are studied.The dissertation can be mainly divided into the following four sections.Firstly,the phase space reconstruction of time series is introduced in the sense of topological equivalence.The geometric invariants such as fractal dimension,largest Lyapunov exponent,approximate entropy,etc.,are employed to characterize the serration dynamics of the high entropy alloys(HEAs)in compress and tensile test under cryogenic temperatures.Jerky evolution of stress,stair-like fluctuation of strain,and scaling relationship between the released elastic energy and strain-jump sizes are detected during plastic deformation of Al0.5CoCrCuFeNi HEA.The negative largest Lyapunov exponent says that the dynamical regime is non-chaotic,which indicates an ordered slip process in compress.For the serrated flow of metastable CoCrFeNi HEA in tensile test,the fractal dimension equal to nearly 1.23,reflects the joint effect of dislocations motion(the one-dimensional linear defect)with the two-dimensional defects(stacking faults and twinning)and three-dimensional phase transition.The positive largest Lyapunov exponent verified the unstable state due to the FCC→HCP phase transition.Secondly,the well defined correlation function between the multi-dimensional observation and the reconstructed phase space is proved to be existed according to the Takens embedding theorem and generalized embedding theorem.And a delay parameterized method for chaotic time series prediction is proposed based on the approximation of correlation function.Furthermore,a prediction system is designed by the combination of the dynamical evolution information and the feed-forward neural network,such as RBFNN and BPNN.Intelligent algorithm including genetic algorithm and particle swarm optimization,are used to obtain the optimal parameters for prediction.The applications of the proposed method on Lorenz chaotic time series,stress-strain signals in material sciences,and stock market index indicate that it can produce efficient and reliable predictions.Next,the analysis and forecasts of the influenza-like illness(ILI)outbreaks in the United States are investigated.Gaussian type function and multivariate polynomial regression are used to calculate the spatiotemporal distribution information.Gaussian type function can well predict the beginning and the end stages of the outbreak of ILI,and the time corresponding to the peak of the outbreaks can also be effectively approximated.The regression equation extracted from the spatial distribution information can be used to fill in the missing data in the corresponding region.In addition,the correlation analysis of the regression equation shows that there is a high correlation between some coastal areas,and the high outbreak areas of influenza like diseases may not be adjacent,which may be related to the transmission method of the virus and the local climate(such as coastal climate).The cluster extracted by correlation analysis can help us establish the recommendation mechanism based on diffusion characteristics.Furthermore,the designed dynamic radial basis function neural network algorithm establishes the correlation function between observation variables and reconstructed phase space with dynamic evolution information.Through the neural network structure,i.e.,the correlation function,the prediction of ILI in the following 52 weeks can be realized,and fitting of the high outbreak stage of ILI has a relatively good performance.In the last chapter,the sparse dynamics method is applied to establish the mathematical model of the data-driven system.To extract the hidden dynamical system from data,the approximation scheme of the derivative,for example forth order central difference,delay coordinates technique,is first selected according to the type of data;then the basis functions library corresponding to the variables of system are constructed,the specific expression of dynamical system can be determined by sparse regression of the parameters.As an application,the control equation extraction of nano-scratching deformation mechanism of amorphous alloy film is studied.According to the limitation of observation dimensions,the fourth-order central difference method and the reconstructed phase space are selected as the approximation of derivative term respectively.The extracted second-order nonlinear differential equation model can well fit the dynamic evolution of observation signal.Meanwhile,the sparse dynamics method can also achieve the approximate expression of the "black box" model in the neural network algorithm.