On Virtual Clearance Monitoring of Steam Turbine by Using Model Order Reduction
Authors: Ito Hiroshi , Hosomi Shoichiro , Tezuka Norikazu , Ishida Tomohiro 
Published: September 2021

Abstract
With the increasing need for flexible operation (shorter startup time and higher load change rate etc.), clearance monitoring between the rotor and the stationary components in steam turbines is becoming more important. This is because as load change rate increases, minimum radial and axial clearances during operation tend to be smaller due to thermal deformation of steam turbines, and the risk of contact between the rotor and the stationary components becomes higher. This situation has accelerated development of clearance sensors. However, it is still difficult to monitor all possible points of contact only with physical sensors due to limited installation location and short lifetime in high temperature environment. From the above background, we have been developing a virtual clearance monitoring (VCM) technique based on a novel data fusion approach that utilizes both physical and data-driven models. Specifically, a reduced order model (ROM) is used as physical model in order to enable real-time prediction with an accuracy similar to that of finite element analysis (FEA). Then, the prediction error of the physical model is corrected by using a residual model built by machine learning from the past clearance sensor values and the corresponding physical model-based prediction results. As will be explained in this report, this technique has an advantage that the clearances can be predicted in real-time based only on operating data such as steam conditions at inlet and outlet, and some temperatures in the parts not modeled in the ROM. Therefore, the virtual sensor based on this technique can be used as a replacement for the physical sensor after it has failed. Furthermore, this technique can also be used to preliminarily study unsteady clearance behavior for inexperienced operating conditions.
This paper describes how to build the ROM from a finite element model for thermal-structural analysis of an entire steam turbine by model order reduction (MOR), and the detail of the VCM technique, and a VCM system installed in a measurement room of a state-of-the-art GTCC power plant manufactured by Mitsubishi Power.
In addition, the verification results of the VCM system are presented. In this research, the ROM and the residual model were built using the data obtained from four operations with different start-up modes each other. Then, VCM was performed for 12 operating cases. As a result, this survey revealed the followings: (1) This system is capable of real-time prediction with output intervals of roughly 2 seconds. (2) As for radial clearance prediction error during rotor rotating, the RMSEs and the absolute values of minimum value errors are less than or equal to 7.2 % and 7.0 % respectively relative to an initial radial clearance value during the steam turbine stopping.
From the above results, we conclude that this VCM technique based on data fusion approach is effective in terms of computational speed and prediction accuracy. This means that if a physical clearance sensor fails, the radial clearance can be continuously monitored by a virtual clearance sensor with a residual model built using the data when the sensor was working normally. In the future, we plan to further improve the accuracy of this technique through improvement in physical modeling.