A Reliability Analysis of the Foundations of Machines and Mechanisms under Periodic Loads by the Criterion of Oscillation Amplitude

The article describes methods of reliability analysis of the foundations of machines and mechanisms under periodic loads with regard to the criterion of oscillation amplitude. These methods take into account the varying volume and quality of initial statistical information about the controlled parameters in mathematical models of limit states at the stages of installation and operation. The controlled parameters in the mathematical model of the limit state are described by probabilistic, possibilistic and combined methods depending on the completeness (or incompleteness) of statistical information. With full statistical information about the parameters (random values) in mathematical models of limit states, probabilistic statistical methods are used for calculating reliability, with the description of parameters by probability distribution functions. As a result, a single-value probability estimate of the level of reliability of the foundation is obtained. With limited (incomplete) statistical information about the parameters (fuzzy variables), possibilistic methods of reliability calculations are used, according to which reliability is characterized by an interval of probabilities where only the boundaries of the interval are known, i.e. the result of the calculations is less informative. When dealing with parameters with both full and limited statistical information, combined methods are used for calculating reliability. The choice of the methods depends on the type of the information available. Due to the fact that some parameters can be described by probabilistic methods, while others by possibilistic ones, it is possible to reduce the range of the calculated reliability interval, for example that of the foundation, and to increase the information value of the calculation results, which will allow the designer to make decisions more objectively.

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