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To ensure reliable and safe functioning of a technical object, it is necessary to assess the current and forecast the future state of it. Let the state of the object be characterized by a set of controlled parameters, for example physical and chemical indicators of a water supply source, vibration of a hydroelectric unit, characteristics of a computer’s central processor, etc. In the process of monitoring, the object’s parameters are recorded at certain points of time and form a system of time series with quasi-periodic dynamics that is periodicity with random change periods. To forecast and assess the future state of such an object, it is necessary to build an adequate mathematical model capable of forecasting the quasi-periodic behavior of the object’s functioning parameters with sufficiently high accuracy. To solve this problem the article proposes to use an image model on cylinders in combination with a pseudo-gradient method to identify model parameters, which will improve the accuracy of modeling and forecasting the state of an object. And for the interpretation of numerical predictions obtained from the models, and the assessment of the state of the object (healthy or faulty), the use of neural network models is proposed. The efficiency of the proposed approaches is demonstrated by the example of forecasting the state of a personal electronic computer (PC).