## 1 Introduction  
The flight service environment spectrum refers to flight time proportions for various working environments in which an aircraft operates during service. In research related to the lifespan of aircraft components, the flight service environment can be characterized by the time history of various flight parameters; that is, some flight parameters' time history characteristics in single or multiple flights, such as altitude, airspeed, yaw angle, vertical overload coefficient, turning radius, or frequency. These time histories can be real data recorded by aircraft, or they can be some generalized parameters after data processing. The definition of the flight service environment spectrum is similar to the random load spectrum in fatigue testing, but a flight service environment has many parameters in one flight profile rather than one (such as only load). It is necessary to consider the flight service environment spectrum when evaluating the life of components in aeroengines. For example, when calculating the load of the main bearing, real flight parameters under different service environments, as input variables, may save the establishment of strong coupling relationships on more than 13 flight parameters [1]. However, the issue of compiling a flight service environment spectrum related to the main bearing load has not yet been addressed. Pressure altitude, as an important indicator of aircraft maneuverability, is currently always used to compile the service environment spectrum of all engine components [2; 3; 4] because all combat or airdrop actions, such as air-air, medium-air-ground, and air-ground states, involve either fast or slow ascent and descent processes. In NATO countries, several special research plans (ENSIP, LUCID, TURBISTAN, Flight-by-Flight, etc.) have been implemented for environment spectrum compilation [5; 6; 7; 8], where the plan TURBISTAN [9; 10] first decomposed maneuvering operations using altitude parameters to determine the load history of engine components. The flight service environments were divided into the initial segment (ground and climb), the middle segment (air stage), and the end segment (landing and ground taxiing stage) based on the altitude. However, no literature is available regarding the compilation of a detailed spectrum for the complex maneuvering motions in the middle segment. In China, many scholars have carried out thorough research on feature extraction and clustering methods for use in the aircraft service environment [11; 12; 13; 14; 15]. References [13; 14; 15] used the maximum altitude of a flight profile as a parameter when compiling the environmental spectrum, where only the limit value of altitude worked and the process characteristics were ignored. However, the latter can more precisely reflect the time-varying service environment. In addition, the method always used by major aircraft companies to classify flight service environments based on training tasks does not meet the requirements of the life analysis of some key components. For example, for main bearings, the compilation of the service environment spectrum needs to consider flight parameters related to them, such as engine rotor speeds, yaw angle, pitch angle, rolling angle, angle velocity in three directions, and overload coefficients, which are closely related not only to the training task but also to the changing details of altitude and Mach. In fact, it is very difficult to extract altitude characteristics when compiling a flight service environment spectrum. There are many factors that affect flight altitude data, especially in complex flight training tasks such as those of military aircraft. Mathematically, the stochastic process composed of altitude samples is non-stationary and non-ergodic. Due to the coupling relationship between flight parameters, most of the transient ascent-descent processes at altitude are accompanied by changes in the yaw angle.