###### Abstract  
There have been steadily growing requirements from the academia and industry, demanding non-invasive methods and reliable measurement systems of research devoted to operational mode analysis (OMA). Due to the simplicity of performing only structures surface vibration measurements, OMA is frequently applied in machine fault diagnosis (MFD) and structure health monitoring (SHM). OMA can handle big structures, such as bridges, buildings, machines, etc. However, there is still an open question: how to properly handle the harmonic effects of rotating components and the difficulty of closely estimating space modes are still a nightmare to deal with. Therefore, the main objective of this paper is to identify the structure of natural frequencies by the regeneration of frequency response functions (FRFs) for complex structures based on OMA. The novelty of our approach is to use the random decrement technique (RDT), correlation function estimation (CFE), and enhanced Ibrahim time method (EITM) to overcome OMA's difficulties and limitations. To reduce further rotational harmonics effects, gear mesh and side band frequencies, digital signal processing techniques based on nothing filters, and lifting analysis techniques were also used. All the experiments were performed at the laboratory test rig and conducted by using three accelerometers, one impedance hammer, one force sensor, and one data acquisition board. To reduce data's variabilities, each test was measured three times for 5 min. The data sampling frequency for all the experiments was 25.6 kHz. To validate the proposed methodology, extensive OMA tests were performed for the generation of FFFs. The measured objects were a steel bar, induction motor, and gearbox. Five structural natural frequencies for the induction motor and eight structural natural frequencies for the gearbox were generated, respectively. operational mode analysis (OMA); vibration analysis; experimental modal analysis; cepstrum analysis; machine diagnosis; random decrement (RD); enhanced time Ibrahim method (ETIM) 2022202020220220220220220220220220220220220220220220220220220220220220222022022022022202202202202220220222022022202202220220222022022202220220222022202220  
structure's natural frequency is closed with the harmonic excitation, it fails to accurately identify the modal parameters. To properly identify the natural frequencies, they proposed a modification of the least-square complex exponential (LSCE), to identify the procedure to include explicitly harmonic signals. The measurement object was a beam with random excitation and several multi-harmonics loads. The applied system was a SIMO system, and they used an enhanced variant of Ibrahim time method (ITM) and LSCE. By applying OMA, it was still a major challenge to handle the MIMO systems and close spaced modes. The reduction of harmonics was studied by [PERSON] et al. in 2004 [3]; they further studied the inclusion of harmonic excitation in OMA, using a new approach of EITM. In this case, they know a priori the harmonic excitation, and it was able to successfully detect the natural frequencies and damping data. The study's object was a steel plate. [PERSON] et al. in 2005 [4] studied the application on OMA based on RD, ITD, and frequency domain decomposition (FDD). The outcomes of their studies were the generation of natural frequencies of a civil structure. At present, however, there is a somewhat limited validation process to quantify the obtained results. A new approach, introducing OMA's technique, based on non-bayesian (stochastic subspace identification), was developed by [PERSON] et al. 2005 [5]; they performed an overview of OMA, with further analysis with four time approaches, i.e., ARMA model-based, NEXT, stochastic realization-based, and stochastic subspace approaches, as well as frequencies approaches, i.e., frequency domain decomposition (FDD). The researchers developed a new approach, concerning blind source separation, for the detection of modal parameters for OMA applications. [PERSON] et al.