# Maintenance Prediction through Sensing Using Hidden Markov Models--A Case Study
## 3 Global [PERSON] [50] states that \"Real-world processes generally produce observable outputs which can be characterized as signals.\" These observable states will be used as input to the HMM model which will later give us the hidden states which, in turn, will correspond to the equipment state. To improve these inputs to the model, a sequence of methodologies is performed to perform the \"optimization\" of the observable states (Figure 1). Figure 1: Methodology for observable states optimization to insert into the HMM. As we can see in Figure 1, the sensor data will be modified to obtain better algorithm efficiency, both in calculation time and global performance. First, the data are collected by sensors over time, which, later, are managed aiming to optimize the observable states. After data collection, these go to the preprocessing stage, where a data preparation is carried on, to improve the quality of the data set. At the end of data preparation, the data are grouped in time intervals and, after, replaced by statistical values representative of each interval. Based on this generation of characteristics, it is possible to extract more information from the data, as the statistical resources, based on the time domain, providing good performance to characterize trends and changes in data [52]. The data are then normalized and inserted into a dimensional reduction model using Principal Component Analysis (PCA). Sizing features through Z-Score standardization is an important preprocessing step to resize features according to a standard normal distribution, with a mean zero and a standard deviation one. In our case, it is important to use the Z-Score standardization to implement PCA method because we are interested in the components that maximize the variance. If one feature varies less than another, because of their respective scales, the PCA defines the direction of the maximum variation that more closely matches the axis, which varies more if those features are unscaled. It is important to standardize the data to make the algorithm more sensitive to the changes that may occur in different measurements. Therefore, standardization is performed because this model requires resources to be on the same scale aiming to find directions that maximize the variation. In this process, we will only obtain the principal components (PCs) for the study and reduction of the dimensionality of the dataset. The observations are now defined in a new space, redefining the axes through the PCs instead of the original variables. In other words, the characteristics of the data will be reduced to reduce the computational load. In this study, the PCA was chosen; it is a very consolidated and easy method to use. It is an unsupervised model that permits to find the most significant coordinate system of the data to find the strongest characteristics of the samples. Additionally, it is not time-consuming, it reduces well the overfitting, and can be used as a noise removal and data compression technique [27; 34; 38; 53]. The elimination of the large part of the experimental noise is possible--the noise originates random errors, which are not correlated with the information contained in the data matrix--improving the numerical stability of the model [36]. Finally, a clustering is performed, which will group similar data and differentiate from data from other data groups. In other words, clustering will group the observations as homogeneously as possible within each cluster and as heterogeneously as possible among the different clusters. In this way, observations of the equipment in good working order will be grouped in a cluster, observations of the equipment in failure will be grouped in another, and so on. Each cluster formed will, in turn, be used as an observable state that will enter the HMM. The method used in this study will be Clustering k-means, which does the grouping using Euclidean metrics.