A gas path diagnostic method based on sparse Bayesian learning is presented. Most gas path diagnostic problems present the case where there are fewer measurements than health parameters. In addition, the measurement readings can be faulty themselves and need to be determined, which further increases the number of unknown variables. The number of unknown variables exceeds the number of measurements in gas path diagnostics, making the estimation problem underdetermined. For gradual deterioration, it is common to apply a weighted-least-square algorithm to estimate the component health parameters at the same time sensor errors are being determined. However, this algorithm may underestimate the real problem and attribute parts of it to other component faults for accidental single fault events. The accidental single fault events impact at most one or two component(s). This translates mathematically into the search for a sparse solution. In this paper, we proposed a new gas path diagnostic method based on sparse Bayesian learning favoring sparse solutions for accidental single fault events. The sparse Bayesian learning algorithm is applied to a heavy-duty gas turbine considering component faults and sensor biases to demonstrate its capability and improved performance in gas path diagnostics.
Kalman filters are very popular in gas path diagnostics. This algorithm estimates the engine state variables to assess engine health conditions and is accurate in tracking gradual deterioration. However, the performance of the Kalman filter deteriorates when an abrupt fault occurs. There could be a long delay with the Kalman filter in diagnosing the abrupt fault. In addition, the Kalman filter may transfer the abrupt fault on to other components. In this article, an adaptive gas path diagnostic method using strong tracking filter is described that can track gradual deterioration and abrupt fault accurately. The strong tracking filter is an adaptive extended Kalman filter, which introduces suboptimal fading factors into the prediction error covariance of the extended Kalman filter algorithm. The suboptimal fading factors automatically increase when an abrupt fault occurs, therefore, more importance is given to the new measurement in state estimation which allows the filter to quickly track abrupt faults. All of the suboptimal fading factors become one when gradual deterioration occurs, and in this situation, the strong tracking filter becomes the common extended Kalman filter to filter the measurement noise. Therefore, the strong tracking filter can track abrupt faults quickly and accurately, filter measurement noise, and obtain noise-free parameter estimation for gradual deterioration. The strong tracking filter is applied to heavy-duty gas turbine gas path diagnostics for a variety of simulated fault cases to demonstrate the capability of the strong tracking filter in accurately tracking gradual deterioration and abrupt fault.
A novel method for measurement selections of gas path diagnostics has been developed. This method is based on the singular value decomposition of the observability matrix of linear systems, which are a good approximation of the nonlinear ones for small deviations. It also employs the concept of'the degree of observability to formulate the criteria. The states with high degree of observability and the measurement sets with high overall degree of observability result in high estimation accuracy in gas path diagnostics. A heavy-duty gas turbine model is used to validate this method. The influence of the gas turbine nonlinearity, the measurement noise, and the overdetermined measurement on degree of observability is analyzed. The overall degree of observability is calculated for different measurement sets of heavy-duty gas turbine. The gas path diagnostics simulations with different measurement sets using the weighted least-squares estimation method and the extended Kaiman filter are conducted. The quality of gas path diagnostics simulation with different measurement sets is assessed and the results demonstrate the capability of the developed method for measurement selections in gas path diagnostics.
A new method of the observable degree analysis based on the singular value decomposition of the observable matrix was proposed. The method can be used to calculate each state's observable degree more correctly. Two commonly used methods, condition number method and singular value decomposition method, of observable degree analysis were united, and the feature of the two methods was analyzed. The proposed method was applied to analyze the states observable degree of a heavy-duty gas turbine at different conditions, and the result can be used to assess the effectiveness of gas path fault diagnostic schemes quantitatively.
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