PSI - Issue 48

Behrooz Keshtegar et al. / Procedia Structural Integrity 48 (2023) 348–355 Keshtegar et al / Structural Integrity Procedia 00 (2019) 000 – 000

353

6

2

   

   

ql

 AsEs AcEc 3.81 1.13

  

  

  0.03

g

(13)

2

There are six normal random variables with properties tabulated in Table 1.

Fig. 2. Roof truss in Example 2

Table. 1. The random variables for roof truss Random variable q(N/m) l(m)

As(m 2 )

Ac(m 2 )

Es(Pa) 1×10 11 6×10 9

Ec(Pa) 2×10 10 1.2×10 9

Mean

20000

12

9.82×10 -4

0.04

Standard deviation

1400

0.12

5.9852×10 -5

0.0048

The reliability results based on the proposed reliability methods are listed in Table 2. It is seen that the HL-RF produces chaotic solutions, whereas the DSTM converges to a reliability index of 2.42. The HS is more stable than the HL-RF but is more inaccurate. The PSO is strongly more accurate than the HS and is more robust than gradient based HL-RF formula. The PSO is as robust as the DSTM but it is more accurate. By comparing the results of DSTM and PSO for this problem, the DSTM provides the reliability index with less call functions than the PSO, while is an advantage of the modified gradient methods that can converge faster than the evolutionary non-gradient approaches.

Table. 2. Reliability results for roof truss example

Error (%)

Method MCS HL-RF DSTM

Iteration

Call function

Reliability index

P f

--

10 7

2.34

0.0096

-- --

Not-converged

Chaos

--

80

2081 3000 3000

2.42 3.24 2.32

0.0077 0.000597 0.002256

3.5 38.4

HS

600 600

PSO

0.9

Example 3: A steel frame showed in Fig. 3 with implicit complex performance function is defined as [7]:   0.05 g The statistical properties of the random variables are tabulated in Table 3. The Reliability index is obtained using the DSTM after 38 iterations with number of call functions equal to 2466 to achieve a stable result of 3.16, whereas the HL-RF method achieves unstable results with a chaotic reliability index. The converged results based on the studied methods for this problem are tabulated in Table 4. As seen, the PSO provides stable result, more accurately. The HS is more robust than HL-RF but is more inefficient and inaccurate, (14)