Abstract
The possibility of applying the theory of stochastic processes for evaluating the dynamic pattern of different states is studied for critical-duty structures. Heterogeneous Markovian processes of technical state transition for metallurgical overhead crane structure, Markovian theorem and Kolmogorov-Chapman equation are analyzed. Markovian chain is reviewed at t →∞, i.e. under marginal steady-state (stabilized) condition. Real values of limit probabilities are obtained for the structure of the metallurgical overhead crane under review. The proposed approach redefines and elaborates the existing methods and procedures for evaluating the technical state of structures and reduces the level of ambiguity associated with such kind of problems.
Highlights
Stochastic processes explore the dynamic evolution of random phenomena [1]
We shall regard the process occurring in this system as a heterogeneous Markovian chain with respective transition matrices [2, 3, 6]: pp(tt) = pp0exp [− ∫0tt λλ(tt)dddd]
The theory of stochastic processes can definitely apply to address the evaluation of the existing technical state of various critical-duty structures
Summary
Stochastic processes explore the dynamic evolution of random phenomena [1]. This particular approach is necessary for addressing various physical, technological and other types of problems. Application of the stochastic process theory [1] and probabilistic risk analysis [2, 3, 13] will allow to elaborate these procedures and apply a more well-reasoned approach to the operation of such structures. We can proceed to solving the practical problem of applying the theory of stochastic processes to the evaluation of the existing technical state of the structure. We shall regard the process occurring in this system as a heterogeneous Markovian chain (one step corresponds to one scheduled inspection of the crane structure after 15 years of operation) with respective transition matrices [2, 3, 6]: pp(tt) = pp0exp [− ∫0tt λλ(tt)dddd]. The use of the above approach definitely elaborates the existing methods and procedures [6, 12] by reducing the entropy of information ambiguity associated with such kind of problems
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