I'm looking into using clustering-based method to detect anomalies in vibration signals. The idea is to extract features for every single sliding time-window of a time series of normal vibration data, and then find clusters of the feature vectors. Given a new period of vibration data, the model will classify the period as anomaly if its corresponding feature vector does not belong to any of the normal clusters.
Is there any literature on under what condition such methods will fail? My intuition is that clustering does not capture time-dependence of data. For instance, if I use Gaussian Mixture Model for clustering and find two clusters $N_1$ and $N_2$, the sliding windows of my normal vibration data may well form an alternating pattern, such as $N_1 N_2 N_1 N_2...$, while an anomalous vibrational time series has pattern $N_1 N_1 N_1...$, even though the data points in the anomalous vibrational data will belong to the normal clusters.
I'm not sure if this intuition is valid, though, for natural vibration. Say, if I plan to use the clustering-based approach to detect anomalies in machine vibration, is it even physically possible to have different vibrations that have same clusters as described above? If it's possible, is there a way to systematically generate realistic vibration data to show the weakness of such clustering algorithms?
