PSI - Issue 5

Jing Zhang et al. / Procedia Structural Integrity 5 (2017) 1176–1183 Xia Yang et al. / Structural Integrity Procedia 00 (2017) 000 – 000

4

1179

30

80

The fast varying part Strain peak 18.1με

10

60

-10

/s

0

20

40

40

20

Strain/με

0

00:00 4:00 8:00 12:00 16:00 20:00 24:00

Time/HH:mm

Fig. 1. Strain peaks induced by vehicle loads of Taiping Lake Bridge (27th December 2015)

0.05 0.1 0.15 0.2

1

Empirical PDF Fitted PDF Empirical CDF Fitted CDF

0.5

PDF

CDF

20 25 30 35 40 45 0

0

Strain peak/με

(a) The mixed distribution of three Normal distributions p 1 =0.3665,μ N1 =18.56,σ N2 =0.94 p 2 =0.4708,μ N2 =22.62,σ N2 =2.09 p 3 =0.1627,μ N3 =32.21,σ N3 =5.45

20 25 30 35 40 45 0 0.05 0.1 0.15 0.2 Strain peak/με PDF Empirical PDF Fitted PDF Empirical PDF Fitted CDF

1

20 25 30 35 40 45 0 0.05 0.1 0.15 0.2 Strain peak/με PDF Empirical PDF Fitted PDF Empirical CDF Fitted CDF

1

0.5

0.5

CDF

CDF

0

0

(b) The mixed distribution of one Lognormal distribution and two Normal distributions

(c) The mixed distribution of one Weibull distribution and two Normal distributions p 1 =0.7593,μ N1 =18.1,σ W1 =5.62,ζ W1 =0.9796

p 1 =0.4056,μ L1 =2.99,σ L2 =0.052 p 2 =0.4385,μ N2 =22.87,σ N2 =2.14 p 3 =0.1559,μ N3 =32.52,σ N3 =5.38

p 2 =0.0953,μ N2 =19.93,σ N2 =0.71 p 3 =0.1454,μ N3 =21.98,σ N3 =1.34

Fig. 2. Strain peaks over 18.1 με fitted by the three mixed distributions

Table 1. Parameters of three parentdistributions Parent distribution P 1 P2 P 3

The first component

The second component

The third component

(i)

0.6

0.25 0.15

0.15

μ N = 30, σ N = 4 μ N = 28, σ N = 2.5 μ N = 20, σ N = 1

μ N =40, σ N =6 μ N =35, σ N =5 μ N =23, σ N =1.5

μ N =26, σ N =0.8 μ L = 3, σ L = 0.2

(ii) (iv)

0.75 0.75

0.1

0.1

0.15

σ w =4.5, ξ w =1.3, μ w =20