# Gas Turbine Off-Design Performance Adaption Based on Cluster Sampling
## 1 Introduction  
Gas turbines, due to its advantages of lower emissions, fast starting-accelerating, high power density [1], and high fuel flexibility [2], have been widely applied in aircrafts, shipping [3] and power generation [4]. Performance estimation [5], operating optimization [6] and diagnostics [7] of gas turbines are important and depend heavily on an accurate gas turbine performance model. The accuracy of the performance model relies considerably on its component characteristic maps, and component maps are obtained in rig tests under different conditions, which can be costly and time consuming [8]. Thus, only component characteristic maps coming from a similar gas turbine can be provided by original equipment manufacturer (OEM) [9]. This is insufficient; as discrepancies caused by manufacturing, assembly deviation, and overhaul of gas turbines will always exist, variations of component characteristic maps between gas turbines are inescapable [10]. To overcome this problem and obtain an accurate performance model, considerable attention has been paid to the research of performance adaption based on operating data. [PERSON] et al. [11] introduced modification factors to modify component characteristic maps and established an optimization procedure to optimize the modification factors. [PERSON] et al. [12] further developed this method by introducing determining corrections and sensitivity analysis. [PERSON] et al. [13] proposed a new scaling method based on system identification, which used component characteristic maps and scaling factors at both design and off-design points. Then, a genetic algorithm (GA) was introduced to this method to create better shapes of the speed lines [14, 15]. [PERSON] et al. [16] proposed adesign-point performance adaption approach by the Newton-Raphson method. Based on this study, a multiple off-design point adaption algorithm was proposed that linearizes the off-design scaling factors around the design point and obtains the optimal result by GA [17]. Furthermore, a nonlinear multiple-points off-design performance adaption was proposed [18]. Then, a least square method was used to determine the search range of the scaling factor coefficients [19]. To improve the accuracy of the off-design performance adaption, [PERSON] et al. [20] introduced elliptic equations to represent compressor maps with seven coefficients to control the shape of the maps, and tested it on a GE (general electric) aerodervative gas turbine [21]. Then, a method considering the rotation of the ellipses and transformation of its coordinates was further developed [22]. [PERSON] et al. [23], considering insufficient information, proposed a new generation method, in which the initial map was obtained according to a set of steady-operating data; then, the coefficients were tuned through sets of transient data. To overcome the zonal distribution effect existing in field data-gas turbine performance adaption, [PERSON] et al. [24] proposed a new metric to evaluate the adaption accuracy and changed the performance parameters at the design point. [PERSON] et al. [25] proposed an enhanced component analytical solution and utilized sensitivity analysis to set the weight coefficient for the tuning factors. Of this research, the majority use optimization algorithms to obtain scaling factors or their coefficients minimizing the total average prediction error of the measurable parameters of random sampling points. However, in the production site, due to the coordination of power grid dispatching, gas turbine generator sets are turned on for a long period of time and turned off for another long period of time. This is reflected on the on-site data as the frequent occurrence of working conditions and less data for other working conditions. At the same time, due to interference, noise, sensitivity, fouling, and erosion, there are no deterministic working conditions, and there will be fluctuations within a certain range reflected in the data [24].