## 1 Introduction  
The overall structure of the global energy consumption market is constantly changing and the proportion of clean energy is increasing due to climate change and air pollution control in recent years. However, clean environmental energy, such as wind energy, tidal energy, water energy, solar energy and others, has a very large limitation due to unstable collection [1], so the supporting effect of thermal power generation for the new power system is still significant. In the global energy consumption market in 2023, the proportion of fossil fuel power generation in the field of power generation still reached about 60%, of which the share of gas turbine power generation with natural gas as fuel was also stable at about 23% [2], and its importance is obvious. The gas turbine has the advantages of environmental friendliness, quick start and stop, easy adjustment, etc. At the same time, the gas turbine power generation cycle is also a relatively clean power generation technology which has a wide range of application scenarios. The relatively high temperature of the gas turbine exhaust is usually around 500 \({}^{\circ}\)C [3], so there is still a wide range of waste heat that is worth recycling. For waste heat recovery system design of a gas turbine, the prevailing coupling cycles are steam Rankine cycle, organic Rankine cycle and S-CO2 power cycle. Steam Rankine cycle is suitable at higher permissible temperatures. In Europe, the United States and Japan, studies have been carried out to increase the efficiency of a gas-steam combined cycle as early as the end of the 20 th century [4]. The organic Rankine cycle is suitable under lower temperatures due to the low decomposition temperature of the working medium [5]. However, the decomposition of organic working medium at high temperature may affect the safety of the whole system. The S-CO\({}_{2}\) power cycle has recently aroused the interest of researchers because of its larger recovery temperature range, smaller size and lightweight system design [6]. For the coupling system of gas turbine power generation and S-CO\({}_{2}\) cycle, most of the researches are still at the stage of system design and analysis. Due to the influence of measurement deviation and data transmission error during actual production and operation, it is difficult to obtain accurate measurement data and make it reflect the real operating state of the system. Therefore, further research is needed to perform accurate performance parameter analysis and error diagnosis identification in the simple coupling system. To solve the problems mentioned above, fuzzy logic [7; 8], genetic algorithms [9; 10], neural networks [11; 12], data reconciliation and other common methods may be used to monitor the performance of thermal system. Among these, data reconciliation technology is very effective in improving the measurement accuracy. Data reconciliation is a method that realizes the coordination and optimization of the input data of the system, reducing various random errors through the model principle and mechanism and various redundant information from the measurement process [13; 14]. Data reconciliation technology can reduce the deviation of measurement data and identify gross errors, which can even obtain complete and accurate system performance parameters. Taking the optimization results after data reconciliation as system input data, the calculation accuracy of system performance analysis and error identification can be improved, and it also lays the foundation for the subsequent improvement of system cycle performance and thermal efficiency. The development of data reconciliation technology has also been through the un-remitting efforts of researchers. In theoretical researches, [PERSON] et al. [15] used graph theory method for data reconciliation calculation and revealed the consistency between this method and the traditional algebraic method in solving data reconciliation problems. [PERSON] et al.