Robust subspace tracking in intelligent fault diagnosis of digital twin gas turbines base on the adaptive Markov transfer

Gas turbines play a crucial role in energy, transport, and the net-zero transition, making secure and efficient operation paramount. Despite advancements in digital twin (DT)-based intelligent fault diagnosis (FD) for gas turbines, real-time accurate condition monitoring and isolation of multiplicative faults remain persistent challenges. These challenges stem from multi-component coupling, the scarcity of labeled fault data, and the presence of data corruption. To address these issues, this study develops an unsupervised adaptive intelligent fault diagnosis strategy employing a five-dimensional DT model and integrating a discrete-time Markov chain with an extended Koopman operator, utilizing subspace tracking techniques. First, a gas turbines state-space prediction model is formulated based on the extended Koopman operator, and in conjunction with a generalized Hankel matrix, a Markov parameter vector and an extended Markov matrix are derived, ultimately yielding a continuous-time nonlinear time-varying state-space system model. Subsequently, utilizing real-time operational data from the gas turbines, the signal principal subspace is updated using Fast Approximate Power Iteration (FAPI) subspace tracking. By aligning this signal principal subspace with the Markov parameter vector and extracting the parameter matrix, online real-time monitoring of gas turbines state parameters is achieved. Furthermore, to enhance robustness against non-standard Gaussian contaminated noise environments, a dynamically adaptive robust subspace tracking method based on α-divergence is proposed. The proposed method's reliability and superiority are demonstrated through extensive experimental results, exhibiting an F1 score above 97 % in all scenarios, which outperforms existing subspace tracking methods under contaminated noise and multiplicative fault conditions.