Practical Inapplicability of Identification Models That Use Gradient Methods for Parameter Adjustment

Abstract – In this paper, it is proved that calculations in identification models described in literature are done in the field of small numbers at the presence of high level of noise. It does not allow to obtain reliable estimations of the first and second derivatives of the Hessian matrix and to determine the movement on the gradient in the direction of decrease of the functional of discrepancy of difference equations. Therefore, the method does not converge. It is based on replacement of difference equations with Diophantine equations. That does not give advantages; the solutions are characterized by algorithmic uncertainty and yield numerical results with an abstract content. Their practical application is impossible without additional decoding. However, it is not done, and the process of identification is incomplete. Any introduction of additional operators in the model, as it is done in stochastic models, leads to structural methodical errors and, as a consequence, to creation of false extrema in functional of discrepancy. This leads to biases in parameter estimations, resulting in numerical results which correspond to physically impossible objects. Analysis of convergence of gradient method on the basis of increasing the number of equations formed on an interval of transient process cannot give reliable conclusions. Because of the non-uniform attenuation of its partial components, the stationary character of behaviour of difference equation solutions is violated. Their chaotic fluctuations lead to fluctuations of discrepancy functional. It contradicts the stationary nature of the identified object and proves the practical inapplicability of the model. Application of methods of statistical hypothesis testing with the use of various laws of probability density distribution in conditions of calculations with small numbers leads to additional distortions of obtained numerical results. Recommendations about the organization of test modes of identification and application of alternative methods for realization of decoding methods are also given