Quickest Joint Detection and Classification of Faults in Statistically Periodic Processes

An algorithm is proposed to detect and classify a change in the distribution of a stochastic process that has periodic statistical behavior. The problem is posed in the framework of independent and periodically identically distributed (i.p.i.d.) processes, a recently introduced class of processes to model statistically periodic data. It is shown that the proposed algorithm is asymptotically optimal as the rate of false alarms and the probability of misclassification goes to zero. This problem has applications in anomaly detection in traffic data, social network data, ECG data, and neural data, where periodic statistical behavior has been observed. The effectiveness of the algorithm is demonstrated by application to real and simulated data.