Wavelet Analysis and Predicting Model Stability

The present article is dedicated to the problem of creating prediction models' of manufacturing processes and providing the conditions of the models stability. Predicting models are increasingly applied in advanced control systems, intelligent systems of information decision making support systems, play a huge role in any activity concerned with signal processing procedures, involving detecting faults of different technological processes and evaluation of the risk potential of critical information infrastructure plants, as well as can be applied in safety threats monitoring systems. A particular class in the series of predicting models is formed by models based on the knowledge about running processes (for instance, regularities revealed from data gathered as a result of the plant performance). In the paper, a virtual “instant” plant model is considered. It is represented under the multi-scale wavelet expansion of input actions vectors and plant output prediction. The considered model provides the prediction without accounting possible states of the prediction ground. To investigate the virtual “instant” model stability, an approach is developed on the basis of the wavelet analysis. Using the approach, prediction model stability conditions are obtained with the focus on the conditions for the approximating and detailing constituent parts for four types of the interrelationship between the input and output memory depth. The paper presents stability conditions of a predicting model, which are developed based on the multi-scale wavelet transform, as well an example of the predicting model applied in the oil refining process.