# Maintenance Prediction through Sensing Using Hidden Markov Models--A Case Study
As noted by [PERSON] et al. [6] and by [PERSON], [PERSON], and [PERSON] [7], a prerequisite for the implementation of effective CBM practices in the industry is an effective diagnosis and prognosis. According to [PERSON] and [PERSON] [8], the CBM decision-making process based on the information obtained from the HMM is adequate to recognize the condition of the equipment. The HHM is a double stochastic process that can define, through probability, the equipment diagnosis, that is, how the machine can go from a good working state to a bad working state and what the statistics are in each state. [PERSON] et al. [7] explain that the HMM has two very useful features when it comes to monitoring CBM equipment: first, they refer to the existence of computationally efficient methods to calculate probabilities (an important feature, as it promises to be an efficient tool for signal processing that can be economically implemented), and second, they mention the existence of efficient techniques that can be used to identify the system health with HMM, that is, they can be used to build equipment models based on data, aiming to identify specific characteristics in the data to be used as health indicators. There are several examples of HMM-based approaches to monitor failure detection [4; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]: [PERSON] [4] uses an unsupervised online learning scheme, where an Adaptive Hidden Markov Model (AHMM) is used to learn online the dynamic changes in the health of the equipment; [PERSON] et al. [6] present a method where several HMMs are used to represent a health state of a metal cutting tool; [PERSON] et al. [7] show, in addition to why the HMM is a model for equipment diagnostics, its use with vibration data to diagnose helicopter gears; [PERSON] et al. [10] use the HMM to detect failures for fluid machines without adequate a priori information about failure conditions; [PERSON] and [PERSON] [12] present a bearing failure detection and diagnosis scheme based on vibration signals; [PERSON] et al. [13] focus on the analysis of the bearing failure diagnosis model concentrated in an HMM model, and compare it with other approaches, namely Multilayer Perceptron (MLP) detection techniques; and [PERSON] et al. [14] present an extensive description of the state of the art of the HMM, also describing how this model can increase the quality of the assessment of Diesel engine conditions and the efficiency of maintenance planning. In relation to the study carried out, this paper demonstrates how by performing a multivariate analysis using several different sensors and with only one HMM it is possible to obtain a diagnosis of the equipment, in this case, a drying press. This approach is used instead of using one HMM for each sensor or multiple HMMs for each sensor, where each HMM represents an equipment health state. In this paper, the steps to be followed to optimize the HMM inputs will be demonstrated, and it will also be shown that through features generation and extracting features (using PCA), it is possible to merge the various sensors. The paper starts with an introduction to the general theme in Section 1. In Section 2, the methodology used to optimize observable states for HMM is explained. Section 3 presents a theoretical framework for each of the steps, including the HMM model itself. Section 4 explains the case study and demonstrates all the steps taken until the equipment is diagnosed. Section 5 discusses the results and explains ideas for future work. Finally, in Section 6, the conclusions of the study are presented.