Sensitive parameter identification and uncertainty quantification for the stability of pipeline conveying fluid

Abstract

Several uncertainty quantification and sensitivity analysis methods are used to determine the most sensitive geometric and material input parameters of a cantilevered pipeline conveying fluid when uncertainty is introduced to the system at the onset of instability. The full nonlinear equations of motion are modeled using the extended Hamilton’s principle and then discretized using Galerkin’s method. A parametric study is first performed, and the Morris elementary effects are calculated to obtain a preliminary understanding of how the onset speed changes when each parameter is introduced to a ± 5% uncertainty. Then, four different input uncertainty distributions, mainly, uniform and Gaussian distribution, are chosen to investigate how input distributions affect uncertainty in the output. A convergence analysis is used to determine the number of samples needed to maintain simulation accuracy while saving the most computational time. Then, Monte Carlo simulations are run, and the output distributions for each input distribution at ± 1%, ± 3% and ± 5% input uncertainty range are found and discussed. Additionally, the Pearson correlation coefficients are evaluated for different uncertainty ranges. A final Monte Carlo study is performed in which single parameters are held constant while all others still have uncertainty. Overall, the flow speed at the onset of instability is the most sensitive to changes in the outer diameter of the pipe.

Appendix

$$\beta = \sqrt[4]{{\frac{m + M}{{EI}}\omega^{2} }}$$

(5)

$$C_{ij} = EI\eta \int_{0}^{L} {\beta^{4} \phi_{j} \phi_{i} dS = } \delta_{ij} \eta \omega^{2}$$

(6)

$$\left( {Cu} \right)_{ij} = 2M\int_{0}^{L} {\phi^{\prime}_{j} \phi_{i} }$$

(7)

$$K_{ij} = \int_{0}^{L} {\left[ {EI\beta^{4} \phi_{j} - \left( {m + M} \right)g\left( {L - S} \right)\phi^{\prime\prime}_{j} + \left( {m + M} \right)\phi^{\prime}_{j} } \right]\phi_{i} dS}$$

(8)

$$\left( {Ku} \right)_{ij} = M\int\limits_{0}^{1} {\phi^{\prime\prime}_{j} \phi_{i} ds}$$

(9)

$$C = C_{ij} + U\left( {C_{u} } \right)_{ij}$$

(10)

$$K = K_{ij} + U^{2} \left( {K_{u} } \right)_{ij}$$

(11)