## 1 Introduction
They discussed the difference between traditional machine learning (ML) and deep learning approaches. For the success of a data-driven approach, a sufficient amount of accurate data must be available for network training. However, industrial plant rotor systems always have insufficient datasets. In that regard, model-based techniques designed for fault identification originating from physical models of rotor systems (complete or partial) have been offered for years. Using model-based techniques, numerous studies have detected rotor faults with success. [PERSON] et al. [15] used a model-based identification approach in the frequency domain to identify an imbalance on a test rig. [PERSON] and [PERSON] [16] used an experimental validation approach to support model-based methods for fault location, severity assessment, and fault classification. [PERSON] [17] applied this methodology to concurrently identify instances of imbalances and cracking within a rotor-bearing system. [PERSON] and [PERSON] [18] employed model-based techniques to detect imbalances and cracks and experimentally validated their imbalance identification results conducted on a test rig. [PERSON] et al. [19] estimated the imbalance and misalignment of a flexible rotating machine based on a single run-down procedure. [PERSON] et al. [2] provided a thorough analysis of a model-based rotating machine identification system. They discussed various methods for deriving foundation models from operational data and subsequently updating them. [PERSON] and [PERSON] used an experimental model-based method to identify imbalance and misalignment issues in a rotor-bearing system [20]. However, there are numerous applications for this technique, such as in the studies conducted by one particular work group [21; 22; 23], who have made significant contributions to the field of rotor fault identification using a model-based method. In a very recent study, [PERSON] et al. [24] derived a novel model-basedapproach in which model parameters such as bearing constants and initial imbalances are identified in the first phase and progressive imbalances based on daily operational data are used to identify them in the second phase. The imbalance can, therefore, be monitored online and in real time. In general, the model-based method yields the most accurate results, which are consistent with the physical theory; however, model derivation and verification processes are extremely time-consuming and must be performed by rotor specialists. Numerous ongoing studies on imbalances in rotating machinery have been performed, spanning a wide range of topics, such as imbalance misalignment [25], imbalance diagnostics [26], modeling methodologies to help with imbalance prediction, and lab-based experimental investigations. There are a number of comprehensive literature studies that outline the range of imbalance prediction research, including those by [PERSON] et al. [27], [PERSON] [28], and [PERSON] et al. [29]. Shaft bowing refers to a deviation from the perfect alignment of the geometrical axis of the rotor shaft. This phenomenon is often attributed to factors such as heat gradients experienced during the initiation and cessation of operation in thermal turbo turbines, material creep, manufacturing discrepancies, and other contributing factors. Depending on the amount and location of the bend, shaft bowing can cause an excessive amount of vibration in a machine [30]. Numerous scholarly studies have been conducted to discern the impacts of shaft bowing in rotating machinery, assess their dynamic properties, and implement suitable corrective measures [31]. The impact of residual rotor bowing on rotor vibrations was examined in a seminal study conducted by [PERSON] et al. [32; 33]. Researchers have studied how residual shaft bowing affects the imbalance response in a simplified rotor model. They examined different combinations of bowing and imbalances to understand their interaction. Additionally, they proposed three distinct balancing methods based on their findings. [PERSON] et al.