Closed Loop Nonlinear System Identification Applied to Gas Turbine Analytics

Intelligent engine condition monitoring and early fault detection is becoming a necessity for modern gas turbines to achieve availability and reliability requirements. Degradation or failure of critical control components, such as the fuel metering valves, negatively affects both reliability and safety. Modelbased approaches for analytics and condition monitoring show great promise with advances in remote connectivity and available computational power. The fuel control loop of a gas turbine engine can be well modeled with a feedback connection of a known controller in series with a block Hammerstein system. In this paper, a method is proposed to use data obtained in closed-loop operation to identify system models from closed-loop operation for use in analytics and demonstrated on high-fidelity simulation data from a TaurusT M 60 gas turbine generator. INTRODUCTION Model-Based Analytics Gas turbine equipment end users operate under increasing equipment reliability and safety requirements. Intelligent engine condition monitoring and early fault detection is becoming a necessity for modern gas turbines to provide diagnostics that prevent unsafe operation, early detection of degradation, and identification of equipment faults that allow preventative maintenance to prevent serious accidents and equipment failure [1]. Since ∗Address all correspondence to this author. the cost of unplanned service interruption is usually significantly higher than the cost of performing preventative maintenance and returning the unit to service [2], the maximization of machine availability is essential. The demand for increased availability coupled with advances in control as well as computational power provides opportunities for advanced condition monitoring and other analytic functions to help achieve availability targets. In tandem with these advances, increased connectivity and remote monitoring provides a flexible infrastructure and natural fit for OEMs to enhance the analytical capabilities and value of their service offerings. Condition monitoring can range from direct physical inspections to indirect model-based methods for assessing the state of the engine systems and components. Of all condition monitoring methods, the model-based approach is the most promising method for the real-time and trend base conFIGURE 1. TURBINE GENERATOR SYSTEM. 1 Copyright c © 2014 by ASME dition monitoring of such complex systems as gas turbine engines [3]. The implementation of model-based approaches for advanced condition monitoring requires balancing the complexity of the model against the required prediction accuracy and information content of available data. Data Sources The data sources available for use in analytics range from industry standard, design-stage, models to remotely collected low resolution operational data. The models required over the life cycle of a gas turbine engine, discussed in [4], vary from the nonlinear performance based high-fidelity models used in the engine design stage to simplified linear models used for control design and condition monitoring applications. There is no one size fits all solution and the target application dictates the data acquisition and model structure requirements. High-fidelity models are complex and rigid in structure, but provide a suitable platform to economically conduct many experiments, that may not be physically feasible, to identify the important relationships and measurements useful for condition monitoring. The design goal is to expose the dominant high-order system dynamics in a methodical manner to generate simple models appropriate for condition monitoring and model-based analytic functions on operational data. Problem Statement The fuel control of a gas turbine engine, depicted in Fig. 1, is perhaps the most critical system, in terms of maintaining system stability and attaining the performance targets of the turbine engine. The critical control element in the system is the fuel metering element or valve. The objective is to estimate a simple, parametrized system model of the fuel control and gas turbine using batch measurements of closed-loop data, for use in system analytics. Here, this is demonstrated using data from a high-fidelity closed-loop simulation. The data consists of the reference speed input r(t), controller output u(t), and system output y(t) along with knowledge of the controller, K(q), and nominal fuel valve model, f0(·). The identification of the static uncertain nonlinearity, f (·), and a nonlinear plant g(x(t)) is approached FIGURE 2. HIGH-FIDELITY SIMULATION BLOCK DIAGRAM. with a Hammerstein model structure and identifying a combined static nonlinear map δ(·) (fuel valve and plant) in series with a linear dynamic system G(q), due to the plant. We apply to the closed loop data direct-approach system identification using a prediction error minimization method. The results are presented using simulation data generated with a first principles, industry standard model of a 5 megawatt, TaurusT M 60, single shaft, simple-cycle, conventional combustion gas turbine, coupled to an electric generator, connected to a variable load. The application example outlines a fault detection metric for identifying fuel valve contamination to data generated with a nominal fuel valve as well as to simulated contaminated fuel valve. Figure 3 demonstrates the comparative fit of measured frequency response function (FRF) from the first principles model to the frequency response of third order linear plant model, identified using the closed-loop Hammerstein model framework presented here. GAS TURBINE MODEL STRUCTURE In modern gas turbines, the fuel control loop, illustrated in Fig. 1, is almost universally implemented using one or several digital feedback control loops. The controller(s) use measurements of shaft speed, engine stage temperatures, and pressures to control fuel pump(s) and valve(s), with partially known, and often nonlinear input-output behavior, to regulate fuel flow into the combustion chamber. The fuel control must meet performance objectives subject to operational constraints for equipment protection and safety.