Research On The Analysis Method Of System Stability Under The Condition Of Uncertain Information

With the development of technology,the system becomes more and more complex.More and more influence factors exist in the system,and there are a lot of uncertainties in influence factor.The existence of these uncertainties will lead to the fortuitous failure of the system.It is of great significance for the study of analysis of the systematic stability and exploration of influence degree of uncertainty on system stability.In the stability analysis of the structure,the correct expression of the uncertain parameter is a prerequisite for the stability of the evaluation structure.However,in fact,stochastic uncertainty and cognitive uncertainty of parameter often exist simultaneously,and parameter distribution often lacks of strict regularity.(For example,a parameter variable basically conforms to a normal distribution,but its mean value is not a certain value instead of drifting in a interval and the variance is not a fixed value instead of drifts in one interval.)The existing methods for dealing with such uncertainties are mostly expressed simply by approximate distribution of parameters or parameter intervals,and there is a phenomenon of information loss,which has certain limitations.For this reason,this paper proposes a system stability analysis method under uncertainty information,introduces probability-box theory,and uses probability-box to wrap up uncertainties of parameter variables to achieve the purpose of expressing and describing these uncertain parameter by rule and line,and it is easy to analysis systematic stability by geometric characteristics of the probability-box and the ability of fusion calculations.First,on the basis of obtaining the system stability equation,modeling probability boxes with each uncertain parameter.Secondly,discretizing probability-box of each parameter by equal confidence,and then computing the Cartesian product by the system stability equation,and then obtaining the probability-box model of the whole system.Finally,taking the zero point as the boundary,it divides the risk area and the stable area,and the area obtained by the integration is used to analysis systematic stability quantitatively.In this paper,the cantilever beam structure is taken as an object of experimental analysis and compared with the traditional analysis method.The experimental results show that this method not only reduces the computational cost,but also improves the accuracy.In order to further analyze the key factors that affect the stability of the system,a sensitivity analysis method is proposed in this paper.The main factors that affect the stability of the system are found out,which provides strong support for minimizing the risk probability of the system.This paper focuses on three aspects,such as modeling of uncertain information parameters,system stability analysis and parameter sensitivity analysis.The main contents are as follows:1.In this paper,the uncertain information in the system is modeled with probability-box,and the modeling algorithm is implemented.Stochastic uncertainty and cognitive uncertainty of parameter often exist simultaneously in a system,the study found that the expression of uncertain information data is unitary in the past,models of these two randomness can be expressed often require more stringent conditions,therefore,this paper uses probability box to describe the uncertainty of parameters in the system.2.This paper purpose a system stability analysis method based on probability-box and an examples is verified with the model in the engineering system.For an engineering structural system,according to the mechanical model of the structure,we can get System stability equation,these unknown parameter in the equation is what we call the uncertain information.This method is applied to cantilever beam structure.Compared with the traditional Monte-Carlo method,it proves the accuracy and practicability of this method.Compared with the method of using evidence theory to analyze stability,the accuracy has been improved.3.This paper purpose a sensitivity analysis method based on fused probability-box,and an example is verified with the model in the engineering system.The purpose is that determine the degree of influence of uncertain information parameters on the target system mode.This method can accurately obtain the sensitivity sequence of each uncertain variable,and it also can accurately obtain the degree of influence of each uncertain variable to the target model.The comparison between the derivation method and the variance method verifies the effectiveness and superiority of proposed method.