Frequent processes of mutual transfer and transformation generally take place between the material flow, the energy flow, and the information flow in complex engineering systems, and complex coupling relationships exist between the different flows. Abnormal coupling of flows will cause flow problems, which can easily lead to the failure of the system functions. To address these problems, in this study, the starting point has been taken as the change in the attributes and types of the study flow, the attributes of the flows have been categorized, and a flow transfer and transformation model, oriented to the flow problem analysis has been proposed. Secondly, based on the analysis of the effect of the attribute changes of flows in complex engineering systems on the generation of flow problems, an innovatively introduced information processing mathematical tool, the polychromatic sets theory, has been used to explore and determine the flow problems existing in complex engineering systems. Further, depending on the different manifestations of flow problems, three solution strategies have been proposed. Finally, the process model of the flow problem judgment and a solution strategy for complex engineering systems has been constructed. The feasibility of the process model has been verified by considering the engineering case of the tubular feeding machine (TFM) system of a large-scale integrated marine resource survey ship.INDEX TERMS Complex engineering system, polychromatic sets, flow problem judgment, solving strategy, tubular feeding machine (TFM) system.