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Multi-sensor data that track system operating behaviors are widely availablenowadays from various engineering systems. Measurements from each sensor overtime form a curve and can be viewed as functional data. Clustering of thesemultivariate functional curves is important for studying the operating patternsof systems. One complication in such applications is the possible presence ofsensors whose data do not contain relevant information. Hence it is desirablefor the clustering method to equip with an automatic sensor selectionprocedure. Motivated by a real engineering application, we propose a functionaldata clustering method that simultaneously removes noninformative sensors andgroups functional curves into clusters using informative sensors. Functionalprincipal component analysis is used to transform multivariate functional datainto a coefficient matrix for data reduction. We then model the transformeddata by a Gaussian mixture distribution to perform model-based clustering withvariable selection. Three types of penalties, the individual, variable, andgroup penalties, are considered to achieve automatic variable selection.Extensive simulations are conducted to assess the clustering and variableselection performance of the proposed methods. The application of the proposedmethods to an engineering system with multiple sensors shows the promise of themethods and reveals interesting patterns in the sensor data.

Multivariate Functional Clustering with Variable Selection and Application to Sensor Data from Engineering Systems