# Maintenance Prediction through Sensing Using Hidden Markov Models--A Case Study
## 5 Discussion  
Observing the matrices, we evidenced, through the transition matrix, that hidden state 1 has a 91.13% probability of remaining in the same state and that it is unlikely to evolve to another state. Thus, as hidden state 1 represents the equipment in order of \"good functioning\", the ideal will always be to remain in this state. Hidden states 2 and 3, on the other hand, have some tendency to remain in the same state or to develop to the previous state, which can happen due to maintenance actions. Regarding the emission matrix, we found that the hidden state 1 occurs in a higher percentage when observing the observable state 1 and it never happens when observing the observable state 3. The opposite happens  
Figure 8: HMM scheme for transition and emission.  
Figure 9: HMM Hidden States using the observable K-means Clustering.  
with the hidden state 3. This makes sense because, as it was described along with this paper, observable state 1 was defined as the observable state that has the highest number of points, and by contrast, observable state 3 occurs the least number of times and, therefore, it is the one that is observed in the highest percentage, when the equipment is defective. Thus, hidden state 3 only occurs when observable state 3 is observed.  
Apparently, the equipment had several alert states that return to a good working condition, in principle through (preventive) maintenance. As for the equipment failure status, this happened several times over the three years, which may signify that the drying press maintenance must be improved.  
This paper tested several observable state \"optimization\" tools to insert into the HMM algorithm to perform the equipment diagnosis. As explained above, there is not a priori information about the equipment failure conditions being not possible, through the Working Orders (WO), to verify the effectiveness of the model. However, through graphical analysis, we can see, through Figure 9, that hidden state 3 happens in situations where the direct observations of the sensors deviate from the expected pattern.  
Regarding the contribution of this model, it allows an online diagnosis of equipment from sensors, making possible the detection of failures without prior information about the equipment's condition. In addition, it is easy to adapt the number of features, depending on the equipment being sensed. Furthermore, the model can be generalized to any number of sensors and any equipment.  
To improve the model in the future, we intend to make a diagnosis and prognosis of the equipment in an operation based on an online algorithm. For that, an Artificial Neural Network class, such as Multi-Layer Perceptron (MLP), may be used to improve the HMM performance. The objective of MLP is to predict which is the next observable state of the three observable states defined to, through the Viterbi algorithm, translating this observable state into a hidden state. Thus, it will be possible to say in advance what the health state of the equipment may be. Furthermore, to retrain the HMM model with the new observable states that may happen, a classification model, such as the Support Vector Machine (SVM), may be used, whose objective is to direct the new observable data read, for the respective cluster. In this way, through the new observable states that are happening, it is possible, through the Baum-Welch algorithm, to go retraining the HMM model. In addition, this study is expected to be extended to the company's five drying presses.