This paper investigates the almost-sure and moment stability of a double nanobeam system under stochastic compressive axial loading. By means of the Lyapunov exponent and the moment Lyapunov exponent method the stochastic stability of the nano system is analyzed for different system parameters under an axial load modeled as a wideband white noise process. The method of regular perturbation is used to determine the explicit asymptotic expressions for these exponents in the presence of small intensity noises.

Electricity is a key energy source in each country and an important condition for economic development. It is necessary to use modern methods and tools to predict energy consumption for different types of systems and weather conditions. In every industrial plant, electricity consumption presents one of the greatest operating costs. Monitoring and forecasting of this parameter provide the opportunity to rationalize the use of electricity and thus significantly reduce the costs. The paper proposes the prediction of energy consumption by a new time-series model. This involves time series models using a set of previously collected data to predict the future load. The most commonly used linear time series models are the AR (Autoregressive Model), MA (Moving Average) and ARMA (Autoregressive Moving Average Model). The AR model is used in this paper. Using the AR (Autoregressive Model) model, the Monte Carlo simulation method is utilized for predicting and analyzing the energy consumption change in the considered tobacco industrial plant. One of the main parts of the AR model is a seasonal pattern that takes into account the climatic conditions for a given geographical area. This part of the model was delineated by the Fourier transform and was used with the aim of avoiding the model complexity. As an example, the numerical results were performed for tobacco production in one industrial plant. A probabilistic range of input values is used to determine the future probabilistic level of energy consumption.