Inverse data transformation for change detection in wind turbine diagnostics

A complex system is expected to show different nominal behaviors under different conditions, and the deviation over time from these nominal behaviors is an indicator of potential faults. The nominal behaviors are either default working states, or learned patterns from extensive historical data. Based on nominal behaviors, change detection is implemented for diagnostics, especially to help detect soft failures (which may degrade, but not preclude, equipment operation). A new technique, the inverse data transformation, is proposed in this paper, which simplifies the abnormality detection with a scaler decision threshold, and the fitting needs to be done only once; otherwise in direct deviation method, multiple curve fittings are required and the decision boundaries are curves, making the decisions on irregularly shaped decision regions difficult and inefficient. Wind turbine operational performance and power curve analysis is utilized as an application example of this technique. Three functions are considered for nominal behavior fitting, and Gaussian CDF function is selected in the inverse data transformation method for its fitting accuracy and one-to-one mapping property in inversion, comparing to Sigmoid function fitting and polynomial function fitting. In the fittings by Sigmoid function and Gaussian CDF function, the models are extended by adding two extra degrees of freedom to account for the shifting. The dynamic fitting is optimized by particle swarm optimization (PSO). Due to the random nature of PSO, multiple trials are carried out, and the parameter variation is small, only from the 9th digit. The states defined by Gaussian CDF method match the real data evenly in the middle region of the power curve, and it describes both the lower and upper kink regions in the power curve consistently. A diagnostic scheme is presented at last to illustrate the usage of the inverse data transformation.