| Since Thoms catastrophe theory was put forward,it is widely applied in various aspects,including meteorological aspect.The influence of meteorological factor is multiple,which means that the weather changes are expressed by numerical as multidimensional time series,and the existing detection methods can only be used to detect the single point of time series,so the paper aims to provide a method,which makes than we can use the existing detection methods to detect the weather changes of multidimensional time series.In this paper,we mainly discuss the Lorenz system.In the second chapter,the paper first gives the numerical solution of Lorenz equation,the initial value is(12,23,56),the integral step length is 0.01,the integral interval[0,10],and numerical solution is the multidimensional time series for mutation detection,and gives the real time nodes of Lorenz rail line mutations,which we compare with the mutation times that are detected by mutation detection method and check the superiority and inferiority of the detected results.In the third chapter,the paper presents two kinds of methods to deal with the multidimensional time series from the second chapter.Method one is the vector inner product method,make the inner product between the multidimensional time series and four groups of basic reference vector(1,0,0)、(0,1,0)、(0,0,1)、(1,1,1),get four groups corresponding single point of time series,then use sliding T-test to detect them,compare the mutation time detected with the real mutation time nodes in the second chapter,we know that when the reference vector is(1,0,0),the detected results are best.Method two is the norm method,chose three basic norms,as 1-norm,2-norm,inf-norm,to deal with multidimensional time series,get three groups corresponding single point of time series,then use sliding T-test to detect them,compare the mutation time detected with the real mutation time nodes in the second chapter,we know that using 1-norm,2-norm,inf-norm to deal with the multidimensional time series,the detected results are relatively inferior.In the fourth chapter,the paper selected three groups of the different initial values,the same integral step length,the same integral interval to solve Lorenz equation,get three groups of numerical solutions,and make the inner product between the numerical solutions with the reference vector(1,0,0),get three groups corresponding single point of time series,then use sliding T-test to detect them,compare the mutation time detected with the corresponding real mutation time nodes,we know that,in general,the detected results are best. |
