Determination of the structure of linear dynamic objects in nonparametric identification problems

The problem of identification of linear dynamic objects is considered. The problem of constructing the parametric structure of dynamic object up to the parameters by using non-parametric models is analyzed. Linear dynamic processes found in various aerospace control loops, for example, in vibration test spacecraft during their production. In this case, the local channel “vibrator - spacecraft” defined by the vibrator and the corresponding sensor signal installed on the spacecraft, can be described by the dynamic difference equations. Since the difference equation of the dynamic object consist of lagging on the appropriate number of cycles of the output variables, the problem reduces to the problem of determining the essential variables. Thus, the method of determining the structure of the dynamic differential equation with up to parameters is based on the application of the rules of allocation of significant variables for nonparametric identification. The essence of this rule is as follows: if, for each variable, a member of the non-parametric estimation assign a optimum ratio blur kernel function in which the difference between the obtained model and the actual output of the object to be minimal, then, is the variable in which the rate will be lower, will contribute more to the formation of the final assessment, and therefore has a greater influence on the output variable. The article deals with the non-parametric model of dynamic objects. The relationship of coefficient blurs kernel function and the influence of a particular variable, measured in non-parametric model output object is investigate. The algorithm of identification of the structure of the difference equation of the dynamic object includes the steps of finding the optimal coefficients blur kernel function for each variable sampling rates, elimination of the unimportant variables, modeling and simulation calculation of the relative error. The algorithm will produce consistently set the above steps until the relative error modeling will not be greater than the value obtained in the previous iteration. Detailed results of numerical study conducted by the methods of statistical modeling of the effectiveness of the proposed method for numerical analogs of differential equations and difference equations for objects with memory are given.