Data-driven models for fault detection using kernel PCA: A water distribution system case study

Abstract

Kernel Principal Component Analysis (KPCA), an example of machine learning, can be considered a non-linear extension of the PCA method. While various applications of KPCA are known, this paper explores the possibility to use it for building a data-driven model of a non-linear system-the water distribution system of the Chojnice town (Poland). This model is utilised for fault detection with the emphasis on water leakage detection. A systematic description of the system's framework is followed by evaluation of its performance. Simulations prove that the presented approach is both flexible and efficient.

Optimising approach to designing kernel PCA model for diagnosis purposes with and without a priori known data reflecting faulty states

“…(9) Having the model defined, one has to define the error in order to match the testing points against the training ones. Following [6], [14] we can use the reconstruction error, regarded as a squared distance between the exact projection of the test data point on all principal components and its projections on the most relevant eigenvectors by using Pythagoras theorem (10):…”

“…It considers two cases: with access to data reflecting the faulty states and without such data. The methods are explained on simple testing example and then verified on case study that is leakage detection in drinking water distribution network [13], [14]. In order to speed up the calculations, they were realized with the use of multi-threaded parallel processing.…”

Fault estimation of nonlinear processes using kernel principal component analysis

“…Different techniques have been proposed to describe the nonlinearities leading to the nonlinear PCA generally using the kernel machines, the so-called kernel PCA (KPCA). Many studies for fault detection based on the KPCA have been proposed [6], [7], [8] and more generally for process monitoring [9], [10].…”

Artificial intelligence methods in diagnostics of analog systems

“…Similarly to SVMs, they transform examples from the original domain to the modified one, where they are easier distinguishable. Applications of PCA are twofold: it is used as a standalone diagnostic method (for instance, analysis of sensor arrays (Nowicki et al, 2012)) and as the preprocessing tool before the training stage of the AI approach (often being the preprocessing stage for an ANN).…”