The emergence of modern technology in the oil and gas sectors presents an opportunity to enhance productivity, minimize environmental impact and optimize the energy efficiency of these facilities, leading to increased economic benefits. In pursuit of sustainable development in gas-turbine operations, this study develops a mathematical model that is validated through experimental tests for monitoring the vibrations of an MS5002B gas turbine located in a gas compressor station. The primary objective is to determine the bifurcation indices, ensuring the continuous stability of the studied turbine's operating state while monitoring its vibrations in real-time.A comparison between the experimental and numerical results of the developed model is validated against real operating data, enabling predictions of the complex dynamic behaviors within the bearingrotor system of the examined turbine. Robustness tests, based on real-time operating data, are conducted to analyze the impacts of undesirable effects that may disrupt the turbine system, as depicted in the bifurcation diagram. This approach facilitates the monitoring of the dynamic behavior of vibratory phenomena in the examined turbine, allowing for the establishment of reliable diagnostic elements to ensure component stability and prevent unscheduled production shutdowns. Ultimately, this approach enhances energy efficiency while delivering environmental and economic improvements.