Information-flow-based Sensitivity Analysis Of Systems

Information flow is an important concept in analysis of system dynamics,and it has a wide range of applications and researches in many academic fields such as system science,meteorology,neuroscience,oceanography,biology,network dynamics,financial economics,statistical physics,turbulence,data science and artificial intelligence,etc.The statistical characteristics and applications of multi-factor information flows based on the single-factor information flow are studied in high-dimensional dynamical systems and an information-flow-based global sensitivity analysis method for multivariate output responses from the perspective of single-factor information flow is proposed.The main work and innovations of this paper are as follows:1.The multi-factor information flow analysis method with respect to absolute entropy are established.According to the underlying mechanism is derived from entropy change and transfer during the evolutions of multiple components,a formalism of information transfer within a high-dimensional deterministic dynamical system for both continuous flows and discrete mappings based on the single-factor formalism respectively is established,with which the corresponding properties are given and the relationship between it and the low-dimensional information flow is analyzed.This work is mainly focused on three-dimensional systems,with the analysis of information transfer among state variables can be generalized to the application of high-dimensional systems by the same derivation procedures.Explicit formulas of high-dimensional information flows are generalized and verified in the classical Lorenz and Chua systems,and the related formulas for characterizing nonlinear strength are given in the application.The uncertainty of information transfer for all variables is quantified by using the high-dimensional formulas,which is benefit us for studying dynamical behaviors as well as asymptotic dynamics of the system.The simulation results show that the high-dimensional information flows of dynamical systems reveal some underlying physical information and can be used to investigate the related problems of uncertainty quantification.2.The generalized multi-factor information flow analysis method with respect to relative entropy are established.The predictability change could come from the evolution itself and a transfer of the evolutions of multiple components for a given component in multi-dimensional dynamical systems.Considering that the invariance upon nonlinear transformation of relative entropy,a generalized multi-factor formalism of information transfer with respect to relative entropy or Kullback-Leiber divergence within a multi-dimensional deterministic dynamical system is established based on the theories of single-factor information flow with respect to relative entropy and multi-factor information flow with respect to absolute entropy.The theoretical properties of the generalized information flow with respect to relative entropy are discussed,with which the relationship between it and the single-factor information flow with respect to relative entropy as well the multi-factor information flow with respect to absolute entropy is analyzed.The information flow formalism with respect to relative entropy from two variables to another variable in three-dimensional dynamical systems is given,as well as the generalized multi-factor formalism of information flow with respect to relative entropy from two variables to another variable in the high-dimensional system and the generalized multi-factor formalisms of information flow with respect to relative entropy among several variables in high-dimensional systems are given.Finally,the applications of the generalized formalisms in R?ssler system and a four-dimensional system are studied,and the simulation results suggest that the generalized formalisms can identify indirect information transfer among variables,which benefit us for further understanding the internal mechanism of complex multi-dimensional dynamical systems.In the meantime,the high-dimensional information flows provide a quantified way of information transfers among variables in complex dynamical systems,so it can be used to investigate the propagation of uncertainties in complex dynamical systems and system prediction,as well the sensitivity analysis of multivariate outputs.3.An information-flow-based global sensitivity analysis method for multivariate output responses is presented.The information transfer formalisms based on the joint probability density function of the system can be utilized to represent the overall uncertainty information of the system with multivariate outputs.The information flow is used as a global sensitivity analysis index in this paper.Combing with the advantages of the information flow,a new global sensitivity analysis method based on the information flow of multivariate output responses is proposed to determine the effects of the uncertainty of the input variables on the uncertainty of multivariate output responses.We illustrate the difference between the sensitivity analysis method proposed in this paper and the correlation coefficient method for linear case simultaneously.Since the uncertainty among variables can be quantified by computing the simple information flow formula,the method not only has no restrictions on input variables and characterizes the complete uncertainty of output responses,but also can be used for sensitivity analysis of experimental data.In the meantime,it is simple to calculate,easy to complete,low in cost,and meets the needs of sensitivity analysis in a big data environment.Finally,the efficiency and applicability of the demonstrted method are verified in analysis of numerical examples and engineering test examples,and the method is applied to analyze the influence of the perturbations from the angle of attack on the aerodynamic experiment results of NACA 0012 in the wind tunnel test.