An engine is the heart of an aircraft. It produces thrust, drives the generator, pumps the hydraulic system and provides compressed air for all the systems on the aircraft. Its health plays an essential role in flight safety. In the past, the standard operation procedure to evaluate the health status of engines usually depended on some specific parameters, like inter-stage turbine temperature, low-pressure spool rotating speed or high-pressure spool rotating speed. Once part of the parameters pass over certain safety boundaries that were previously set by the manufacturers or the operators, the engine would be regarded as an unhealthy engine. Nevertheless, in practical applications, such threshold-style mechanism cannot reflect engine fault immediately and therefore could lead to potential flight risk. To solve this issue, a precise forecast model of the engine has to be established. Consequently, this research is dedicated to develop algorithms for engine modeling as well as the identification of optimal parameters. For the TFE-731 engine, there are three section models considered, including low pressure compressor (LPC) model, high pressure compressor (HPC) model and overall turbofan dynamics model. Those models are derived with the consideration of physical isentropic compression equation as well as a data-driven regression technique. Experiments show that a precise modeling fitting can be achieved by using regression analysis and nonlinear optimal parameter estimation. Finally, to compare the prediction stability and accuracy, associated training models using neural network (NN) are also presented. Comparison studies verify that the proposed method is able to achieve stable as well as accurate TFE-731 real-time response prediction and monitoring. INDEX TERMS Turbofan engine modeling, parameter identification, fault monitoring.