Sensor fault identification based on kernel principal component analysis

We propose a sensor fault identification method for process monitoring using kernel principal component analysis (kernel PCA). Although it has been proved that kernel PCA shows the outstanding fault detection performance for nonlinear process, the fault identification method has rarely been found. Using the gradient of kernel function, we define two new statistics which stand for the contribution of each variable to the monitoring statistics, Hotelting´s T² and squared prediction error (SPE) of kernel PCA model. The proposed statistics have similar concept to the contributions in linear PCA and they are directly derived from the mathematical formulation of kernel PCA. Since the proposed fault identification method does not require any approximation or reconstruction procedure, it is easy to understand and it can significantly reduce the loss of information. To demonstrate the performance, the proposed method is applied to a simulated non-isothermal CSTR process. The simulation results show that the proposed method effectively identifies the source of various types of sensor faults.