Abstract
The objective of the present work is to develop a novel approach for combining in an ensemble multiple base clusterings of operational transients of industrial equipment, when the number of clusters in the final consensus clustering is unknown. A measure of pairwise similarity is used to quantify the co-association matrix that describes the similarity among the different base clusterings. Then, a Spectral Clustering technique of literature, embedding the unsupervised K-Means algorithm, is applied to the coassociation matrix for finding the optimum number of clusters of the final consensus clustering, based on Silhouette validity index calculation. The proposed approach is developed with reference to an artificial casestudy, properly designed to mimic the signal trend behavior of a Nuclear Power Plant (NPP) turbine during shut-down. The results of the artificial case have been compared with those achieved by a state-of-art approach, known as Clusterbased Similarity Partitioning and Serial Graph Partitioning and Fill-reducing Matrix Ordering Algorithms (CSPAMETIS). The comparison shows that the proposed approach is able to identify a final consensus clustering that classifies the transients with better accuracy and robustness compared to the CSPA-METIS approach. The approach is, then, validated on an industrial case concerning 149 shut-down transients of a NPP turbine.
Highlights
In industries such as nuclear, oil and gas, automotive and chemical, equipments are subjected to several causes of performance degradation and exposed to faulty conditions, e.g., presence of manufacturing defects, unexpected interactions with the environment, wear and tear (Bolotin & Shipkov, 1998; Muller, Suhner, & Iung, 2008; Baraldi, Di Maio, & Zio, 2012; Baraldi, Di Maio, & Zio, 2013c)
The approach is, applied to a real industrial case concerning 149 shut-down transients of a Nuclear Power Plant (NPP) turbine: different base clusterings representative of different groupings of the shut-down transients of the turbine are obtained by using multiple different sources of data, i.e., vibration, turbine shaft speed, vacuum, and temperature signals, and a final consensus clustering is obtained that gives the optimal grouping of the shut-down transients of the NPP turbine, in terms of groups separation and compactness
Spectral Clustering to transform S into a normalized laplacian matrix L rs, and compute its spectrum information, 3) a clustering algorithm, e.g., the K-means algorithm, that is fed with the eigenvectors calculated in the previous step 2), to find the final consensus clustering, and 4) the Silhouette index to quantify the goodness of the obtained clusters
Summary
In industries such as nuclear, oil and gas, automotive and chemical, equipments are subjected to several causes of performance degradation and exposed to faulty conditions, e.g., presence of manufacturing defects, unexpected interactions with the environment, wear and tear (Bolotin & Shipkov, 1998; Muller, Suhner, & Iung, 2008; Baraldi, Di Maio, & Zio, 2012; Baraldi, Di Maio, & Zio, 2013c). Several methods have been used to obtain the final consensus clustering, for example Relabeling and Voting (Ayad & Kamel, 2010), Co-association Matrix (Vega-Pons & Ruiz-Shulcloper, 2011), Genetic Algorithms (Ghaemi, bin Sulaiman, Ibrahim, & Mustapha, 2011; Chatterjee & Mukhopadhyay, 2013), Finite Mixture Models (Topchy et al 2004; Topchy et al 2005), and Graph and Hypergraph partitioning (Karypis, Aggarwal, Kumar, & Shekhar, 1997; Strehl & Ghosh, 2002; Vega-Pons & Ruiz-Shulcloper, 2011). The approach is, applied to a real industrial case concerning 149 shut-down transients of a NPP turbine: different base clusterings representative of different groupings of the shut-down transients of the turbine are obtained by using multiple different sources of data (features), i.e., vibration, turbine shaft speed, vacuum, and temperature signals, and a final consensus clustering is obtained that gives the optimal grouping of the shut-down transients of the NPP turbine, in terms of groups separation and compactness.
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