The installed positions of three domestic turbo-shaft engines mounted on a certain type of ship-borne helicopter interfere with the intake air flow of the engines, resulting in a decline of engine performance after initial installation. Due to the difference of load and adjustment method under the bench and installed conditions, it is necessary to study the change in gas turbine power rather than output shaft power of the engine before and after installation to evaluate the engine initial installed power loss. In this paper, quantum-behaved particle swarm optimization (QPSO) is applied to optimize the calculation of gas turbine power at different steady states based on the component-level aerodynamic thermal model of gas generator. Then, extreme learning machine (ELM) is adopted for regressive identification of the established gas generator state assessment model based on data mining and the identification model is applied to engine installed condition. Finally, statistical analysis of engine initial installed gas turbine power loss at three installed positions is carried out, respectively. Results show that the values of engine initial installed gas turbine power loss at three installed positions all conform to the normal distribution, the mean values are 1.658%, 9.828%, and 5.089%, respectively, and a confidence interval with 95% confidence level of the mean values are (1.388%, 1.928%), (9.178%, 10.478%) and (4.308%, 5.870%), which can provide references for determining the power monitoring thresholds after engine installation.