Acknowledgements

The authors acknowledge the funding received from the Center for Oil and Gas-DTU/Danish Hydrocarbon Research and Technology Center (DHRTC). The authors are also grateful to Professor Jørgen Amdahl for his support regarding the Finite element analysis with USFOS.

### Conflict of interest

schedule. The SHM installation time differs depending on the thresholds (see Table 6). A higher threshold means that the SHM system is installed closer to the end of service life. With increasing annual system failure probability threshold, the

(a) Expected total costs for base scenario, inspection and repairs strategy (S1), and SHM, inspections, and repairs (S3). (b) Value of information and action based on SIM strategies for different annual system failure

SHM outcome Annual system failure probability threshold 6.00E-05 tSHM = 6 years

Theory, Application, and Implementation of Monte Carlo Method in Science and Technology

High performance ð Þ Z<sup>1</sup> 0.175 0.0991 0.0497

Low performance ð Þ Z<sup>3</sup> 0.272 0.3973 0.5419

tSHM is SHM installation time for a given annual system failure probability threshold.

The probability of SHM outcomes for different annual system probability thresholds.

7.00E-05 tSHM = 8 years

0.553 0.5036 0.4084

8.00E-05 tSHM = 11 years

The values of information and action (VOIA) of the two SIM strategies are shown in Figure 10. It is observed that increasing the system failure probability threshold will reduce the value of information and action. With a higher threshold, inspection and monitoring are performed later in the service life, which reduces the benefits due to a higher annual system failure probability during the remaining service life compared to a lower system failure probability threshold. It is also observed that the VOIA of the SIM strategy SHM, inspection and repair (S2) is higher than the inspection-only strategy (S1) for all investigated system failure probability thresholds. This shows that information from SHM system can enhance the value of the SIM, i.e., reduce the expected total cost. In this example, the cost of

probability of obtaining low performance outcome (Z3) becomes higher.

system failure is dominating the expected total cost over the service life.

In the present analysis, physics-based numerical models of the load, structural behavior and for the integrity management have been utilized in combination with response surface techniques and Monte Carlo simulation. An application of a physics-based digital twin model is illustrated for the structural and integrity management analysis of a specific jacket structure. The loading is represented by a response surface with the basic environmental parameters as input. The control

4. Summary and conclusions

As-expected performance

ð Þ Z<sup>2</sup>

Table 6.

Figure 10.

172

probability thresholds.

There is no conflict of interest.

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