CATASTROPHE THEORY METHODS IN DESIGNING TECHNOLOGICAL MACHINE CABINE PROTECTIVE STRUCTURES
This paper deals with the estimation of reliability measures in terms of the catastrophe theory. The cusp catastrophe is considered, control parameters are viewed as stationary random processes (functions) and a problem of overshoot of random function is formulated in the first part of the paper. Analytical equations can be applied to define the reliability function, failure probability (cusp catastrophe probability), mean operating time to failure. The statistical linearization method is used to determine random process characteristics (mean value, dispersion). The possibility of applying catastrophe theory methods for designing elements of technological machines and equipment is analyzed at the next stage of the research, wheeled skidder roll-over protective structure is used as the example. This approach enables to carry out statistical analysis of balance near critical points. The obtained expressions can be applied to estimate the reliability function from the perspective of the catastrophe theory.