A Novel Ensemble Clustering for Operational Transients Classification with Application to a Nuclear Power Plant Turbine

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.

Matrix Completion with Ordering Relation Constraints and its Applications

We relax the equality constraints in the very general and well-known affine Schatten p-norm minimization problem into complete loss function-based constraints. Owing to the imposed equality constraints, existing methods only have limited degree of model flexibility, via their optimization of the objective energy function. By our proposed transformation, the decision variables in the objective function can directly achieve L0 norm minimization via the process of enumerating the matrix rank (i.e. matrix ordering constraint). We show that, our new objective function is still reasonable, and its minimum can be obtained by a more general form of the Fixed-Point Continuation framework with almost the same computational cost at each matrix order enumeration. Experiments show that, our algorithm has good performance compared to its predecessor over some datasets and applications.

Implementing Sparse Matrix Ordering Using Hypergraph Partitioning

Matrix ordering is a key technique when applying Cholesky factorization method to solving sparse symmetric positive definite system Ax = b. Much effort has been devoted to the development of powerful heuristic ordering algorithms. This paper implements a sparse matrix ordering scheme based on hypergraph partitioning. The novel nested dissection ordering scheme achieve the vertex separator by hypergraph partitioning. Experimental results show that the novel scheme produces results that are substantially better than METIS.

The Zoltan and Isorropia Parallel Toolkits for Combinatorial Scientific Computing: Partitioning, Ordering and Coloring

Partitioning and load balancing are important problems in scientific computing that can be modeled as combinatorial problems using graphs or hypergraphs. The Zoltan toolkit was developed primarily for partitioning and load balancing to support dynamic parallel applications, but has expanded to support other problems in combinatorial scientific computing, including matrix ordering and graph coloring. Zoltan is based on abstract user interfaces and uses callback functions. To simplify the use and integration of Zoltan with other matrix-based frameworks, such as the ones in Trilinos, we developed Isorropia as a Trilinos package, which supports most of Zoltan's features via a matrix-based interface. In addition to providing an easy-to-use matrix-based interface to Zoltan, Isorropia also serves as a platform for additional matrix algorithms. In this paper, we give an overview of the Zoltan and Isorropia toolkits, their design, capabilities and use. We also show how Zoltan and Isorropia enable large-scale, parallel scientific simulations, and describe current and future development in the next-generation package Zoltan2.

An Approximate Minimal Elimination Ordering Scheme

Matrix ordering is a key technique when applying Cholesky factorization method to solving sparse symmetric positive definite system Ax = b. In view of some known minimal elimination ordering methods, an efficient heuristic approximate minimal elimination ordering scheme is proposed, which has the total running time of O(n+m). It is noteworthy that the algorithm can not only find a good ordering efficiently, but also achieve the result of symbolic factorization simultaneously.