Table 1 Summary of the probability distribution of input variables for Monte Carlo simulation
From: Machine learning-assisted optimal schedule of underground water pipe inspection
Symbol | Physical Meaning | Type of distribution | Mean | Standard Deviation |
|---|---|---|---|---|
\({E}_{p}\) | Pipe material elastic modulus | Normal | 165,000 | 33,000 |
\(\alpha\) | Toughness correction coefficient | Uniform | 10–13.5 |  |
\(S\) | Toughness exponent | Normal | 1.0 | 0.1 |
\({a}_{1}\) | Constants to determine \(\beta\) | Uniform | 0.3–0.5 |  |
\({b}_{1}\) | Normal | -0.25 | 0.03 | |
\(p\) | Internal pressuring | Normal | 0.45 | 0.12 |
\(D\) | Internal diameter | Normal | 200 | 11.43 |
\(t\) | Wall thickness | Normal | 10 | 0.44 |
\(a\) | Final pitting rate constant | Normal | 0.09 | 0.009 |
\(b\) | Pitting depth scaling constant | Normal | 5 | 2.0 |
\(c\) | Corrosion rate inhibition factor | Normal | 0.1 | 0.05 |
\({K}_{m}\) | Bending moment coefficient | Lognormal | 0.235 | 0.05 |
\({C}_{d}\) | Calculation coefficient | Lognormal | 1.32 | 0.2 |
\({B}_{d}\) | Width of ditch | Normal | 500 | 114.3 |
\({K}_{d}\) | Defection coefficient | Lognormal | 0.108 | 0.0216 |
\({I}_{c}\) | Impact factor | Normal | 1.5 | 0.375 |
\({C}_{t}\) | Surface load coefficient | Lognormal | 0.12 | 0.24 |
\(F\) | Wheel load of traffic | Normal | 65,000 | 20,000 |
\(A\) | Pipe effective length | Normal | 6100 | 200 |
\(\Delta T\) | Temperature differential | Uniform | -10–0 |  |
\({a}_{n}\) | Width of pit | Uniform | 3–5 |  |