PSI - Issue 40

V.N. Syzrantsev et al. / Procedia Structural Integrity 40 (2022) 411–417

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V.N. Syzrantsev et al./ Structural Integrity Procedia 00 (2022) 000 – 000

In modern methods of calculation of loading and prediction of the products service life the external load is presented in the form of a loading stepped cyclogram [Zahiri (2017), Kapur (1977), Collins J.A. (1981)]. The magnitude of the cyclogram steps and their relative duration are determined on the basis of the known parameters of the adopted law of external load distribution. Knowledge of the cyclogram allows the methods developed in the fatigue theory to calculate the value of the load (stress), equivalent to the given loading block set by the cyclogram. This approach allows taking into account an operating condition of the product and predicting the service life by the number of strain cycles prior to failure of the product according to the fatigue strength criterion, using equivalent stresses and based on the fatigue curve. If during the product operation the process of its loading is not reduced to a regular one [Sokolov (2017)], then the solution to the problem of the service live prediction is impossible. The current paper presents a solution to two problems. Based on the use of nonparametric statistics [Vapnik (1999), Simakhin (2006), Porshnev (2014), Syzrantseva (2017), Baptista de Souza (2018)], the first problem regards a procedure for determining the stepped cyclogram parameters for the case of setting an external load in the form of a finite length values sample. The implementation of the procedure ensures building a cyclogram for any random law of external load distribution, regardless of its complexity. The solution to the second problem allows determining the duration of the cyclogram steps in the numbers of strain cycles, rather than in the form of relative values. This problem is solved on the basis of using the information obtained with special means of fatigue damage sensor [Kopnov (2017, 1992), Troshchenko (1985), Bojko (1981)], in the course of products operation.

Nomenclature p

pressure values in gas pipeline

mechanical stress



smoothing parameter (Parzen-Rosenblatt bandwidth)

h n K

kernel function

information functional

J

sample variance

n D

FDS

fatigue damage sensor electrical resistance

R

2. Loading cyclogram step magnitude for the case of random external loading setting in the form of a finite length sample with an unknown distribution law We regard the procedure for determining the loading block cyclogram step magnitude on the example of daily registration of pressure values in gas pipeline p i , 1, 365 i n   during a year. With the known geometrical parameters of the pipe: the outer diameter ( D ) and wall thickness (  ), we calculate the stresses occurring in the pipe wall based on p i :     / 2 i i p D      , 1, 365 i n   . (1)

Fig.1 reflects the process of variation of these stresses during a year for one of the gas pipeline compressor stations, which was shown earlier in the work of Syzrantsev (2019).