###### Abstract  
A growing interest in intelligent fault detection may sometimes lead to practical issues when existing malfunctions reveal analogous indications and the number of observations is limited. This article addresses the classification problem of two identical malfunctions, i.e., unbalancing and shaft bow in rotary machines, where only 56 observations were utilized for the training. The faulty systems are modeled in ABAQUS/CAE; a data set for each fault is created by simulation under various physical and operational conditions employing the uncertainty concept. The wavelet time scattering (WTS) technique extracts low-variance presentations from signals. With respect to the classification procedure of the faulted rotor systems, two models are examined with the extracted features from WTS as the input. Initially, a long short-term memory (LSTM) network is trained and tested, and then, the capability of a support vector machine (SVM) model is inquired. Ultimately, the classification models are trained and tested using the raw time series data and the extracted features to compare the effectiveness of the suggested methods, i.e., WTS. The employed approach for feature extraction demonstrated remarkable effectiveness in addressing a potential hurdle in identifying faults in rotating systems: the ability to differentiate between unbalanced and bowed rotors, irrespective of the classification model utilized. rotary machines; unbalancing; shaft bow; FE analysis; wavelet time scattering; long short-term memory; support vector machine +
Footnote †: journal: Applied Sciences  
_Applied_  
_Acticle_  
Classification of Unbalanced and Bowed Rotors under Uncertainty Using Wavelet Time Scattering, LSTM, and SVM  
[PERSON], [PERSON], N.  
if any abrupt changes occur in the under-monitoring parameters (for instance, in the regression model) [1]. After noticing a change in the machine's operation, the next step is fault diagnosis, which allows the type, severity, location, and root of the fault to be determined. Numerous malfunctions, including misalignment, shaft bow, shaft crack, defective bearings, and unbalance, can arise in rotary systems. Some of these faults can only be fixed if they are diagnosed early on as ignoring them can have disastrous repercussions [2]. Symptoms can be extracted and compared to the fault constitution, failure criteria, damage theories from standards, and literature findings to detect a fault. However, because the symptoms of some malfunctions are very similar, it can occasionally be challenging to distinguish between them. Rotor systems with bowed and unbalanced rotors are a striking example. Finding the differences in the time domain is incredibly difficult citing the literature, and there are also a lot of unknowns in the frequency and time-frequency domains. Almost all rotating objects, from car rims to sophisticated industrial turbines, are thought to suffer from unbalancing as the most frequent type of damage in such systems. An uneven mass distribution that prevents the center of mass and volume from aligning is the definition of this flaw. This deficiency can cause fatigue load and, if not corrected, can lead to other defects, such as bearing defects and shaft cracks [3]. Myriad research has been carried out in an attempt to identify and correct this failure [3,4]. Studies on fault detection in rotor systems fall into two broad categories: transient and stationary responses. Investigation into the transient responses of a rotating system focuses on the startup or shut-down of the machine. The dynamic behaviors of a misaligned, unbalanced, and mechanically loosed rotor system were described by [PERSON] and [PERSON] [5] using wavelet transform. The study of the run-up signals was performed both theoretically and experimentally. The presence of the aforementioned faults was demonstrated by the appearance, location, and magnitude of peaks associated with the second subcritical speed.