The main objective of this paper is to describe the state of the art of the calibration and certification of industrial sensors, giving an approach on how companies can manage the sensors’ calibration, namely the ones that are incorporated in the equipment. For any industry it is essential to make products that satisfy the customers in terms of quality and, simultaneously, to be competitive in the market. The data obtained from the sensors placed in the equipment is one of the sources that helps to increase the performance, adding value for the competitiveness of the company in the market. Sensors are responsible, in many sectors, to guarantee equipment availability and product quality. In this way, the certification of the company and of the equipment, not only guarantee quality and prevent unwanted and unforeseen costs, but also gives company credibility, namely from the customer's point of view. This paper focus on the state of art of industrial metrology, namely sensors, standards and measuring tools, calibrations and the certification of calibration. It also includes a theoretical section about sensors, types of sensors, their operation and characteristics. Next, it is presented the theme of metrology and the measurement science, responsible for ensuring the quality and veracity of the data sent by the reading equipment. It also addresses the importance of metrological traceability and certified management systems, which are required to certify the sensors calibration, in order to guarantee the effectiveness of the measurements and, consequently, the rigor of operation of the associated quality system.

Condition-Based Maintenance (CBM), based on sensors, can only be reliable if the data used to extract information are also reliable. Industrial metrology plays a major role in ensuring the quality of the data collected by the sensors. To guarantee that the values collected by the sensors are reliable, it is necessary to have metrological traceability made by successive calibrations from higher standards to the sensors used in the factories. To ensure the reliability of the data, a calibration strategy must be put in place. Usually, sensors are only calibrated on a periodic basis; so, they often go for calibration without it being necessary or collect data inaccurately. In addition, the sensors are checked often, increasing the need for manpower, and sensor errors are frequently overlooked when the redundant sensor has a drift in the same direction. It is necessary to acquire a calibration strategy based on the sensor condition. Through online monitoring of sensor calibration status (OLM), it is possible to perform calibrations only when it is really necessary. To reach this end, this paper aims to provide a strategy to classify the health status of the production equipment and of the reading equipment that uses the same dataset. A measurement signal from four sensors was simulated, for which Artificial Intelligence and Machine Learning with unsupervised algorithms were used. This paper demonstrates how, through the same dataset, it is possible to obtain distinct information. Because of this, we have a very important feature creation process, followed by Principal Component Analysis (PCA), K-means clustering, and classification based on Hidden Markov Models (HMM). Through three hidden states of the HMM, which represent the health states of the production equipment, we will first detect, through correlations, the features of its status. After that, an HMM filter is used to eliminate those errors from the original signal. Next, an equal methodology is conducted for each sensor individually and using statistical features in the time domain where we can obtain, through HMM, the failures of each sensor.

The availability maximization is a goal for any organization because the equipment downtime implies high non-production costs and, additionally, the abnormal stopping and restarting usually imply loss of product’s quality. In this way, a method for predicting the equipment’s health state is vital to maintain the production flow as well as to plan maintenance intervention strategies. This paper presents a maintenance prediction approach based on sensing data managed by Hidden Markov Models (HMM). To do so, a diagnosis of drying presses in a pulp industry is used as case study, which is done based on data collected every minute for three years and ten months. This paper presents an approach to manage a multivariate analysis, in this case merging the values of sensors, and optimizing the observable states to insert into a HMM model, which permits to identify three hidden states that characterize the equipment’s health state: “Proper Function”, “Alert state”, and “Equipment Failure”. The research described in this paper demonstrates how an equipment health diagnosis can be made using the HMM, through the collection of observations from various sensors, without information of machine failures occurrences. The approach developed demonstrated to be robust, even the complexity of the system, having the potential to be generalized to any other type of equipment.

Data is an important resource for gaining knowledge about the behavior and condition monitoring of machines, enabling the estimation of parameters and the prediction of failures. However, in industrial environments, sensor interruptions often create gaps in the time series, which affects the reliability of the data. To overcome this challenge, this paper proposes an imputation strategy based on recurrent neural networks, in particular long short-term memory (LSTM) models, within a multivariate encoder–decoder architecture. This approach utilizes correlations between variables to reconstruct missing values, resulting in more complete and robust datasets. Experimental results with multivariate time series show that the proposed method achieves accurate imputation, with errors as low as RMSE = 2.33 and $R^2$ = 0.90 for some variables. Comparisons with alternative architectures, including GRU and Dense networks, show that LSTM excels in specific cases (e.g., VL3, $R^2$ = 0.45), while the Dense architecture provides more stable performance across most variables. In particular, the Dense model achieved the best overall balance between accuracy and robustness, reaching RMSE = 2.33 and $R^2$ = 0.90 for the best-performing variables, while the LSTM achieved the lowest error values in targeted scenarios, confirming its suitability for capturing complex temporal dependencies. Overall, this study highlights the feasibility of using recurrent neural networks to exploit temporal correlations for reliable data recovery, even under conditions of signal interruption in factory environments.

The maintenance paradigm has evolved over the last few years and companies that want to remain competitive in the market need to provide condition-based maintenance (CBM). The diagnosis and prognosis of the health status of equipment, predictive maintenance (PdM), are fundamental strategies to perform informed maintenance, increasing the company’s profit. This article aims to present a diagnosis and prognosis methodology using a hidden Markov model (HMM) classifier to recognise the equipment status in real time and a deep neural network (DNN), specifically a gated recurrent unit (GRU), to determine this same status in a future of one week. The data collected by the sensors go through several phases, starting by cleaning them. After that, temporal windows are created in order to generate statistical features of the time domain to better understand the equipment’s behaviour. These features go through a normalisation to produce inputs for a feature extraction process, via a principal component analysis (PCA). After the dimensional reduction and obtaining new features with more information, a clustering is performed by the K-means algorithm, in order to group similar data. These clusters enter the HMM classifier as observable states. After training using the Baum–Welch algorithm, the Viterbi algorithm is used to find the best path of hidden states that represent the diagnosis of the equipment, containing three states: state 1—“State of Good Operation”; state 2—“Warning State”; state 3—“Failure State”. Once the equipment diagnosis is complete, the GRU model is used to predict the future, both of the observable states as well as the hidden states coming out from the HMM. Thus, through this network, it is possible to directly obtain the health states 7 days ahead, without the necessity to run the whole methodology from scratch.