Interval Reliability Analysis of Parameters of Section of Main Beam

Abstract:

In the calculation of the reliability of hydraulic, due to extensive uncertainties, there are lots of errors in probabilistic reliability analysis. In this paper, by comparing the non-probabilistic reliability index of different function, we get the advantages and disadvantages of one-dimensional optimization algorithm and method of Monte Carlo, and compare the functions of each variable of main beam to obtain the influence of the precision of the variables.

• Periodical: Applied Mechanics and Materials (Volumes 644-650)
• Pages: 4991-4994
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.644-650.4991
• Online since: September 2014
• Authors: Jian Fang Zhou*, Guang Ran Lu
• Keywords: Interval Analysis, Main Beam, Monte Carlo Method, Non-Probabilistic Reliability, One-Dimensional Optimization Algorithm

References

[4] , 5, 6], we can get   295. 005. 0 R RK  , 2MMK  . R, M, b and h can be written as R rc RRR  , M rc MMM  , b rc bbb  , h rc hhh  , 22.

[1] RRc .

[22] [1] RRr  , 22.

[1] MM c   , 22.

[1] MM r   , 22.

[1] bbc   , 22.

[1] bbr   , 22.

[1] hhc   , 22.

[1] hhr   . Substituting R, M, b, h, Eq. 2 and the standard values of them into Eq. 1, the function of one-dimensional optimization algorithm can be rewritten as  .

[2] [1] [2] [1] [2] [1] [2] [1] [2] [1] [2] [1] [2] [1] [2] [1] 95. 005. 0.

[2] [1] [2] [1] [2] [2] [2] [2] [00]                                               R K R M h b M R          (3) Substituting Eq. 2 and the standard values of them into Eq. 1, the function of Monte Carlo method can be rewritten as             .

[8] 1195. 005. 0.

[2] [2] [2] [2] [00]    kHkKB R kM RkRkM  (4) Function of bending. The function can be changed to form of bending as.

[62] [01]  M bh RMRWM (5) Substituting R, M, b, h, Eq. 2 and the standard values of them into Eq. 5, the function of one-dimensional optimization algorithm can be rewritten as  .

[6] [2] [1] [2] [1] [2] [1] [2] [1] 95. 005. 0.

[2] [1] [2] [1] [2] [1] [2] [1] [2] [1] [2] [1] [2] 222.

[2] [2] [01]                                                             hbR K M M h b R          (6) Substituting Eq. 2 and the standard values of them into Eq. 5, the function of Monte Carlo method can be rewritten as              0.

[48] 1195. 005. 0.

[6] [2] 222.

[2] [2] 2222.

[1]     K hbR kMhbR kHkBkRkM  (7)  kR ,  kB are random variables of interval  1， ,  1， , k is the number of variables we take. Comparing Eq. 3, Eq. 4, Eq6 and Eq. 7, we can conclude that one-dimensional optimization algorithm and the method of Monte Carlo don't have the problem of interval expansion. According to the process of each method, when the number of variables of function is little, One-dimensional optimization algorithm is a good method; when there are lots of variables, the computation of One-dimensional optimization algorithm becomes very large, so the method of Monte Carlo is the better. Cross section of I-shaped When the cross section is I-shaped, there are many variables, so it is better to calculate the non-probabilistic reliability index with the method of Monte Carlo. In Fig. 2, B is the width of flange, t is the thickness of flange, b is the thickness of stiffener, h is the height of I-beam. Fig 2 The geometric characteristics of the section are as follows:             412.

[22] [12] [2] [3] [3] thBtBt th b Ix ,    .

[2] [3] [3] 622.

[6] thBtBtthb Mh W M S   Set  21 RRR ， ,  21 MMM ， ,  21 bbb ， ,  21 hhh ， ,  21 BBB ， ,  21 ttt ， . 2.

[1] RR  , 2.

[1] MM  , 21 bb  , 21 hh  , 21 BB  , 21 tt  . Combined with references [7, 8] and some manufacturing errors, we can get the interval of each variable,  [0. 7, 0. 95],  [0, 0. 9],  [0. 84, 0. 96],  [0. 96, 0. 99],  [0. 955, 0. 975],  [0. 88, 0. 98]. And the approximate relationships of the variables of cross section also can be solved as 230.

[1] [2] hb  , 25.

[2] [2] hB  , 220.

[1] [2] ht  . According to references [5, 6], we can get 22.

[1] bbK   , 22.

[1] hhK   , 22.

[1] BBK   , 22.

[1] ttK  . Substituting them into Eq. 1, we can rewritten the function as                           .

[20] [25] [3] 205.

[4] [10] [30] [40] [1] [2] [1] [2] [1] [2] [1] [25] [3] [40] [1] [5] [1] [2] [20] [1] [2] [1] [60] [1] [1] 95. 005. 0.

[2] [2] [3] [3] [2] [3] [3] [2] [2] [0]                                                   kt khktkB kt kB kt kh kb K R khkM RkRM      (8)  kR ,  kM ,  kb ,  kh ,  kB ,  kt are random variables of interval  1， ,  1， ,  1， ,  1， ,  1， ,  1， , k is the number of variables we take. As the accuracy of the method of Monte Carlo is k1 , in order to ensure the accuracy, we take 10 10k . The dates can be solved with MATLAB, do some regression analysis on the dates, the charts and regression models are as follows.