A rollout approach for condition-based maintenance of large multi-unit systems with economic dependence

With advancements in sensor technology, real-time monitoring of machine health conditions allows us to perform condition-based maintenance (CBM) for multi-unit systems. The maintenance decision of a unit is usually dependent on other units in a multi-unit system, inducing an exponentially large state space, which makes CBM of large multi-unit systems a very challenging engineering problem. In this work, we first propose two heuristic decision policies for multi-unit systems, namely the binary action policy and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> -policy. Then we propose a multi-step lookahead rollout approach using the two heuristic policies to solve the challenging CBM problem. By applying the binary action policy, we can effectively reduce the action space and thus reduce the computational load in the rollout, while the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> -policy can be an excellent base policy for the rollout to improve upon. The theoretical gap between the proposed rollout approach and the optimal policy is also derived. The study further shows extensive experimentation to demonstrate the effectiveness of the proposed lookahead rollout approach for solving the CBM problem for small (3 and 5 units), medium (10 and 15 units), and large (20, 30, 40, and 50 units) scale systems.