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Ensuring the accuracy and adequacy of mathematical models based on neural networks is an insufficiently studied area of modeling complex multifactor models based on a limited amount of input data. The article presents the results of studies of randomly organized test samples that complement the training set to the total amount of set of precedents provided for the construction of a mathematical neural network model of the object. It is shown that the adequacy of the neural network model is achieved by agreeing on the size of the set and the expected accuracy of the model on a given set of procedures. The formulation of the optimization problem for adequate neural network models is formulated. The results obtained significantly expand the approaches to increasing the reliability of neural network models.

The article provides a rationale for identifying objects based on wave signatures. Wave signatures in the article are limited to the acoustic range of vibration. The results of experimental studies based on modeling the dynamic processes of propagation of complex excitations in samples of various configurations and with the presence of various defects using the signature of acoustic oscillations excited in the objects of study are presented. As such objects are presented parts of engineering production. These studies confirm the possibility of complex diagnostics of objects with their subsequent use in product quality control systems, in particular, to reduce the level of peak values of residual stresses in body parts during multi-frequency vibro-processing.