The task of constructing diagnostic models for nonlinear dynamics objects solved in this work. The reasons for increasing the dimension of the modern diagnostics objects description and related problems of using existing diagnostics methods are considered. The purpose of this work is to increase the accuracy and reliability of nonlinear dynamic objects diagnosing by forming diagnostic models in the conditions of increasing the dimension of the objects description for creating effective tools for automated systems of technical diagnostics. It is offered a broad overview and classification of methods for reducing the dimension space of diagnostic features including nonlinear dynamic objects with continuous characteristics and unknown structure, which can be considered as a “black box”. The forming diagnostic models method of nonlinear dynamic objects based on the combination of spectral characteristics obtained as the result of continuous models transformations: wavelet transformations coefficients and models moments of different orders is proposed. The family of diagnostic models is proposed as combinations of dynamic objects spectral characteristics with weak nonlinearity. The hybrid method of forming diagnostic models based on the combination of spectral characteristics suggested. The method consist of sequential application of feature filtering for forming primary feature space, construction of secondary feature space using the spectral transformations and diagnostic model construction by complete bust of secondary features. It is developed a detailed algorithm for constructing diagnostic models using the proposed hybrid method. The suggested method has been tested on real-life task of diagnosing a non-linear dynamic object – a electric motor. Primary diagnostic model of the electric motor taken on the base of indirect measurements of the air gap between the rotor and the stator of the motor. Diagnostic models constructed by combining the spectral characteristics of continuous models. The diagnostic models family of the switched reluctance motor is offered. The method is demonstrate more independence of the accessibility indicator then existing methods of the diagnostic feature space biulding: the samples, the moment and the coefficients of wavelet transformations of the primary diagnostic models.

The features of the use of the theory of integral series in applied problems of identification of nonlinear dynamic systems in the field of diagnosing the state of cutting tools are considered. The prospects for developing a method for estimating the states of cutting tools based on indirect measurements using integral non-parametric dynamic models based on experimental input-output data using test pulse effects on the cutting system are substantiated. This approach allows increasing the efficiency of diagnosis by reducing the amount of calculations, as well as, the reliability of the diagnosis by simultaneously taking into account the nonlinear and inertial properties of the system in integrated non-parametric dynamic models. In addition, the models in question are capable of describing faults caused by both changes in the system parameters and its structure, as well as can be used in test and functional diagnostics. A method has been developed for building information models of cutting tool states based on indirect measurements using test pulse effects on a cutting system in the form of loads with impacts and recording system responses, on the basis of which information models are built in the form of multidimensional transition functions. A block diagram of the organization of the experiment “input-output” in the framework of the problem of diagnosing the state of the tool under the conditions of pulse effects on the cutting system to obtain theprimary diagnostic information is proposed. The methods of forming test pulse loads of the cutting system by successive insertion of the cutting tool into the workpiece with different cutting depths, with variable feed and with variable cutting duration are considered.The computational experiment demonstrates the advantages of information models in the form of multidimensional tran-sition functions for modeling nonlinear dynamic systems in problems of diagnosing the states of cutting tools. It has been established that multidimensional second-order transition functions can be used as an effective source of primary data in the construction of au-tomated technical diagnostics systems.

The features of using the theory of Volterraseries and neural networks in problems of nonlinear dynamic systems model-ing are considered.A comparative analysis of methods for constructing models of nonlinear dynamic systems based on the theory of Volterra series and neural networks is carried out;areas of effective application of each method are indicated. The problem statementis formulated, consisting in the creation of a mathematical apparatus for transforming models of nonlinear dynamic systems derived from the Volterra series apparatus into an artificial neural network of a certain structure.The three-layer structure of a direct signal propa-gation neural network has been substantiated and investigated forrepresent nonlinear dynamic systems. It is outlined a class of systems that can be efficiently approximated by this network.The dependence of the Volterra kernelscoefficients and the weighting coefficients of the hidden layer of the three-layer forward-propagation neural network is established.An algorithm for constructing an artificial neural network based on the Volterra series is given.The results of computer simulation of nonlinear dynamic systems using the Volterra neural network and direct signal propagation neural network are presented. The analysis of experimental data confirms theeffectiveness of using Volterraneural networks in problems of modeling nonlinear dynamic systems.Conclusions and recommendations on the effec-tive use of Volterra neural networks for modeling nonlinear dynamic systems are made.

In this work, the problem of diagnostic models constructing under conditions of description dimension increase in the modern diagnostic objectssolves. As a diagnostic objects considers the nonlinear dynamics objects with continuous characteristicsand an unknown structure, which can be considered as a “black box”. The purposeof the work is to increase the reliability of the diagnosis of nonlinear dynamic objects by forming diagnostic models under conditionsof the objects description dimensionality increasing. A review of methods for reducing the dimensionality of the diagnostic features space is given. A method for the constructionof diagnostic models of nonlinear dynamic objects with weak nonlinearity on the basis of univariate and multivariate analysis of variance as a filtering stage of signs is proposed. A step-by-step algorithm for the constructionof diagnostic models using the proposed method is presented. On the example of the task of technical diagnosis a jet engine, diagnostic models are constructed on the basis of univariateand multivariate analysis of variance of continuous models. A family of diagnostic models of a jet engine is proposed.