(373o) Distributionally Robust Optimization Production and Maintenance Schedules
The problem of combined production and maintenance optimization has recently been addressed by various authors (Zagorowska, Thornhill, Haugen, & and Skourup, 2018) (Escobet, Puig, & Nejjari, 2012) (Langeron, Grall, & Barros, 2015) (Salazar, Weber, Nejjari, Theilliol, & Sarrate, 2016). In previous work (Verheyleweghen, Srivastav, Barros, & Jäschke, 2019), we proposed a solution approach based on Markov chains. Given a Markov chain representation of the system degradation, the production rate and the inspection and maintenance frequency are adjusted until the optimal economic performance is found. We proposed to reformulate the problem by approximating the discontinuities of the optimization problem to make it numerically tractable. The final optimization problem is a mathematical program with complementarity constraints (MPCC). The complementarity constraints are relaxed and penalized, so that the problem can be solved using off-the-shelf optimization software (IPOPT (Wächter & Biegler, 2006)). A quasi-global solution is ensured by using a multi-start approach.
However, an accurate Markov chain representation of the system might not be available in practice. Mechanistic models of the system degradation are usually not available except for specific cases, and sufficient degradation data is often not available to develop data-driven models. Consequently, the result from the optimization may not be truly optimal due to the high uncertainty in the Markov model. To remedy this, we propose to consider the transition rates in the Markov chain to be uncertain, but bounded. We formulate a distributionally robust version of the original problem, such that the result will be robust to uncertainties in transition rate of the systemâs Markov chain, and solve it using a scenario-based approach.
We apply the method to the case study of a subsea oil and gas production and processing system. For subsea systems, unplanned maintenance interventions are very costly and must consequently be avoided. Mechanistic degradation models for subsea equipment are typically not available due to the complexity and uniqueness of such systems. At the same time, data-driven degradation models are not available due to poor data and lacking instrumentation. We show that our method results in better performance than a traditional time-based / periodic maintenance schedule, even in the case where the true transition rates are not known exactly. References
Escobet, T., Puig, V., & Nejjari, F. (2012). Health Aware Control and model-based Prognosis. Mediterranean Conference on Control & Automation (MED) (pp. 691-696). Barcelona: IEEE.
Langeron, Y., Grall, A., & Barros, A. (2015, August). A modeling framework for deteriorating control system and predictive maintenance of actuators. Reliability Engineering& System Safety, 140, 22-36.
Salazar, J. C., Weber, P., Nejjari, F., Theilliol, D., & Sarrate, R. (2016). MPC framework for system reliability optimization. In Z. (. Kowalczuk, Advanced and Intelligent Computations in Diagnosis and Control (pp. 161-177). Springer.
Verheyleweghen, A., Srivastav, H., Barros, A., & Jäschke, J. (2019). Combined Maintenance Scheduling and Production Optimization. 29th European Safety and Reliability Conference. Research Publishing.
Wächter, A., & Biegler, L. T. (2006). On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming. Mathematical Programming, 25-57.
Zagorowska, M., Thornhill, N., Haugen, T., & and Skourup, C. (2018). Load-sharing strategy taking account of compressor degradation. 2nd IEEE Conference on Control Technology and Applications. Copenhagen.