Complexity of periodic sequences of large-scale rotating machinery system coupled by multi-fault

Taking the steam turbine cracked rotor system coupling multi-fault as an example, this paper reports systematic numerical experiments exploring two-parameter periodic complexification cascades. Specifically, we report high-resolution phase diagrams predicting and describing how the periodic sequences unfold over a quite extended range of parameter planes. Surprisingly, such diagrams reveal that the distribution of periodic sequences either agrees well with the characteristics of "eye"of chaos, or is characterized by the derived Farey sum tree and the bidirectional symmetrical Stern-Brocot sum tree. These cascades show that the frequent occurrence of transient multi-period motion is a generic feature for the large rotating machinery system with multi-fault. And the paper obtains a cluster of sequences of the Farey sum tree and the Stern-Brocot sum tree specially suitable for the large nonlinear and nonautonomous systems, which can provide a powerful reference for failure prediction and parameter matching.