Differentiating between expanded and fault conditions using principal component analysis

An adaptive non-parametric model (ANPM) has been developed for condition monitoring and applications within prognostics. The ANPM has the ability to monitor systems while adapting to expanded conditions. This ability is useful in uncertain systems where the range of the model could be exceeded by the system when under non-fault conditions. Differentiating between expanded and fault conditions is essential to the ANPM. A method for differentiating between expanded and a fault condition for use in an adaptive model is described. Statistical process monitoring methods using principal component analysis (PCA) have been extensively studied and heavily applied within the chemical industry. A thorough literature review is given on the past applications of such methods, highlighting the applications strengths and weaknesses. A comparison between traditional fault detection and monitoring techniques and the newly proposed expanded process differentiation technique is discussed. Adaptive modeling requirements in a dynamic environment are shown to extend beyond the traditional modeling requirements. The basic approach to PCA is described, with a detailed description of the differentiation method. The Hotelling's T (2) statistic and the squared prediction error, also known as the Q statistic, are used as indicators of the condition of the system. Dependence on the internal linear relationships of the data is discussed, and kernel principal component analysis is described as a solution to difficulties posed by nonlinear relationships. This multivariate differentiation technique is applied to a simulated data set and is shown to correctly differentiate between expanded operating conditions and faulted conditions in an adaptive environment.