## 4 Findings from the Literature Review
### Topic 2--Multiphase Processes and Variable Batch Time Production  
This topic presents the highest number of contributions. This makes it more complex to analyze. The first theme in this topic is phase partitioning, which is closely linked to the concept of the batch and the concept of the production phase. Batch processes often have the characteristic of being multi-phase and clustering algorithms focus on this. An interesting algorithm is the density peaks clustering [36] that manages not only the individual phases but also the transition between them. A problem in phase partitioning is that some techniques, such as fuzzy c-means clustering, require an a priori definition of the number of phases to be identified. This is not always possible. To overcome this limitation, an adaptive fuzzy c-means is proposed [37]. The variable batch duration time leads to a difficult or impossible phase analysis based on its duration. Sequence-constraint fuzzy c-means handles this situation [2]. In this contribution, in addition to uneven batch durations, attention is also paid to the identification of steady and transitional phases within production batches. This latter feature is also the focus of analysis in other contributions, which propose, for example, kernel entropy component analysis as an algorithm for phase partitioning [38], based on the divergence of kernel entropy. Specific subjects in this topic are bearings, data denoising, and vibrations. Bearings, as mentioned above, have been a much-investigated subject, with focuses on specific characteristics. Bearing-related contributions use vibration as a central parameter and the problem of noise and its consequent data denoising as a research focus. In these contributions, with an unusual application, a k-means clustering helps to evaluate the efficacy of the proposed model (e.g., a denoising model) [39]. Another contribution, again with the help of k-means, suggests the application of K-SVD-based sparse representation method clustering to implement dictionary learning and extract information from vibration impulses [40]. Another contribution proposes the application of clustering based on spectrum overlap coefficient and kurtosis index to implement the extraction of periodic pulses from bearing vibration signals [41]. This last contribution highlights another of the keywords presented for this topic, namely the topic of periodic impulses, which are signals that presumably indicate the presence of a fault [41]. Other concepts that appear in this topic are the previously mentioned data denoising, signal decomposition, self-organizing maps, and wavelet transforms. Specifically, there are some contributions with the joint application of signal decomposition approaches and self-organizing maps for fault diagnosis, with the ensemble empirical mode decomposition [42] as well as wavelet transform [43,44]. Another contribution in this topic highlighting the presence of noise is [45], in which spectrum entropy clustering is applied to extract features to be used for fault diagnosis analysis in a gear system. Another solution proposes the application of a recursive clustering algorithm for diagnostic analysis [46]. Clustering for noise management is important because it allows analyses to be implemented without having prior knowledge of the process, e.g., applying the algorithm of mean shift clustering [47]. Two other keywords that carry a common concept are kurtosis and spectral kurtosis (SK). One of the previously mentioned contributions already highlighted the concept of kurtosis, specifically by using a kurtosis index for the process of extracting periodic vibration impulses [41]. In another contribution, kurtosis is used to create two indicators of the health status of a grinding chatter, defining a kind of kurtosis possibility density function benchmark to compare the kurtosis of the test data. In this context, clustering, specifically k-means, has the role of assessing the goodness of the results [48].