Machine learning of a Bayesian neural network with gamma distribution for stability assessment of a monorail crane

The subject of study in this article is a model and method for training a Bayesian neural network to predict the stability of a monorail crane based on the boom's position along the rail track, considering possible deformations under load. The goal is to develop a model and method for training a Bayesian neural network to predict the stability of a monorail crane. To achieve this goal, the following tasks were solved in the study: a mathematical model for predicting the stability of a monorail crane based on the boom's position along the rail track, considering possible deformations under load using the finite element method, was defined; a Bayesian neural network model and a Bayesian neural network training algorithm were defined; and the effectiveness of the proposed Bayesian neural network for predicting the stability of a monorail crane was trained and evaluated. To conduct the study, methods from the following theories were used: Bayesian theory and Bayesian statistics; artificial neural networks and deep learning; theory of numerical methods; and theory of Markov chains Monte Carlo. Based on the analysis, a mathematical model of the stability of a monorail crane by the boom's position along the rail track, considering possible deformations under load, was obtained using the finite element method. The gamma distribution was chosen as the basic distribution for the Bayesian neural network model, and the posterior distribution was obtained according to Bayes' theorem in logarithmic form. The proposed training method involves updating matrices with weight coefficients using the Metropolis – Hastings method, and the feasibility of updating the network is calculated based on the analysis of the difference in posterior distributions for the network states before and after the update. The following results were obtained: training the Bayesian neural network using the proposed method shows that the model makes significant corrections in the parameters, which is a sign of effective training, along with the error value approaching zero. In the conclusions, the scientific novelty of the results obtained is as follows: a new model and method for training the Bayesian neural network are proposed for predicting the stability of a monorail crane based on the boom's position along the rail track, considering possible deformations under load.