Fuzzy numbers calculations as help in fatigue reliability estimation

Fuzzy numbers and fuzzy arithmetic were introduced in order to analyze and manipulate approximate numerical values. In modern complex and large-scale systems we often have to deal with imprecise data. The reasons may be: different experience of people operating the system, not well-known area of knowledge, too many parameters to get them together in short time. One of such problems is increasing safety requirements of structures. It induces necessity to take into consideration the random nature of variables in the fatigue design. Analysis of real structures and their fatigue properties is a big computational problem. In this paper we present how we can use fuzzy numbers as tool for fatigue analysis of structures. The data used to describe a problem-the probability of failure for critical locations of hydraulic cylinder-are statistical. The main problem is to estimate critical areas of cylinder. Given probabilistic data were used in order to design a membership function of fuzzy number. Thus further calculations could be done with use specific operations defined on a specific model of fuzzy numbers-ordered fuzzy numbers. The calculation of fatigue life using fuzzy numbers set is illustrated with analysis of hydraulic cylinders. Damage mechanics approach is used in fatigue analysis with fuzzy numbers set of hydraulic cylinder.