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data are collected through appropriate sensors installed on critical components and stored in a suitable device. Due to the high sampling frequency allowed by advanced data acquisition tools, and potential measurement errors and noise, signals that are collected by sensors do not provide direct comprehension of the health state of equipment. Therefore, signals are first analysed in time, frequency, and/or time-frequency domains, in order to extract relevant features that highlight a clear distinction among different health conditions of the equipment. Subsequently, the relationship between the extracted features and the corresponding health status of the system is established (diagnostics). Finally, based on the fault modes, the degradation rates and the failure thresholds (FT) identified during the diagnostics, the remainingusefullife (RUL) of the monitored equipment is predicted (prognostics) as the length of time between the current time and the time at which the FT is estimated to be exceeded. In the literature, a large number of methods that are related to machine learning (ML), artificial intelligence (AI), and statistical learning theory (SLT) are available to conduct any of these processes [ 5 – 9 ]. However, most applications: (1) are oriented either to diagnostics or prognostics, which makes it difficult to practically understand the relationship between the two different tasks [ 10 ]; and, (2) adopt a supervised learning approach, i.e., require many training data corresponding to component health conditions for model construction [ 11 ]. Unfortunately, conducting lab tests, e.g., accelerated testing, is expensive from both economic and time consumption points of view; in addition, there exist fault behaviours that cannot be known a priori, especially for new machinery produced on order. These reasons limit the implementation of PHM to real industrial contexts.
Uncertainty management is an important aspect of health monitoring, due to the presence of several unknown factors that affect the operations of the system of interest. Therefore, it is not only important to develop robust algorithms for diagnosis and prognosis, i.e., accurately perform diagnosis and prognosis in the presence of uncertainty, but also im- portant to quantify the amount of conﬁdence in the results of diagnosis and prognosis. This can be accomplished by quantifying the uncertainty in fault diagnosis and prognosis (future performance prediction and remainingusefullife). It is important to perform such uncertainty quantiﬁcation (UQ) online so as to enable in-ﬂight decision-making capabilities. Sankararaman and Mahadevan [5, 6] developed statistical (both frequentist and Bayesian) approaches to quantify the uncertainty in the three steps of diagnosis (detection, isola- tion, estimation) in an onlinehealth monitoring framework. There have also been a few papers [7–10] which discuss uncertainty propagation in prognosis; however, many of these papers are either suitable only for ofﬂine prognosis or they do not provide a comprehensive treatment of uncertainty. For example, the “Damage Prognosis Project” at Los Alamos National Laboratory  dealt with prognosis mainly in the context of ofﬂine testing and decision-making. Guan et al.  investigated Bayesian and maximum relative entropy methods for continuously updating the uncertainty in damage assessment, in the context of ofﬂine prognosis. Often, all the different sources of uncertainty - physical variability, data uncertainty, and model uncertainty - are not rigorously accounted for during prognosis; while most studies focus only on parameter variability and loading variability, the other sources of uncertainty are ignored. Sankararaman et al.  explained and addressed this issue in detail by identifying and accounting for the different types of uncertainty, the methodology was still developed in the context of ofﬂine testing. Therefore, there are several challenges relating to the topic of prognostics uncertainty quantiﬁcation, and it is clear
Over recent decades, much research has been implemented to develop health monitoring methods for rotating machinery, especially bearings. Compared to faultdetection, the literature of prognostics and healthmanagement is relatively limited, and effective implementing of prognostic techniques is still lacking. The increased interest in machinery prognostics has resulted in many successful tools, models and applications in the past few years. Basically, there are three types of prognostic approaches that can be employed to predict the RUL; namely, data-driven methods, physics-based models and hybrid models. Data-driven approaches utilize the historical failure data of the machine and/or similar machines to estimate how much time is left until a system malfunction occurs. This method does not require an in-depth understanding of the physics of systems under study. Physics-based approaches predict the remaininglife according to propagation of the damage mechanism (i.e., physics of failure). A hybrid approach uses both a data-driven and physics-based method so as to achieve an improved predictive performance in terms of a more improved predictive accuracy than that of the single method.
Abstract Reliability of prognostics and healthmanagementsystems (PHM) relies upon accurate understanding of critical components’ degradation pro- cess to predict the remainingusefullife (RUL). Traditionally, degradation pro- cess is represented in the form of data or expert models. Such models require extensive experimentation and verification that are not always feasible. An- other approach that builds up knowledge about the system degradation over the time from component sensor data is known as data driven. Data driven models, however, require that sufficient historical data have been collected. In this paper, a two phases data driven method for RUL prediction is presented. In the offline phase, the proposed method builds on finding variables that contain information about the degradation behavior using unsupervised vari- able selection method. Different health indicators (HI) are constructed from the selected variables, which represent the degradation as a function of time, and saved in the offline database as reference models. In the online phase, the method finds the most similar offline health indicator, to the onlinehealth indi- cator, using k-nearest neighbors (k-NN) classifier to use it as a RUL predictor. The method finally estimates the degradation state using discrete Bayesian
In recent years, harnessing of wind through off-shore wind turbines has increased significantly. However, wind energy industries are experiencing longer downtimes, high maintenance costs and less reliability. As the wind energy industries are located in remote and unmanned regions, it is very difficult to implement reactive and preventive maintenance strategies. In order to make wind energy competitive and economically viable, condition based maintenance is being employed, which allows the scheduling of maintenance thereby reducing the unexpected downtimes . Condition monitoring (CM) systems consists of two sub-systems, namely, fault diagnosis and fault prognosis. Fault diagnosis is defined as detection of physical fault in a mechanical system and classification of the fault type whereas fault prognosis is concerned about predicting the remainingusefullife (RUL) of the mechanical system . Previous researchers have used vibration analysis in order to diagnose the defect present in the wind turbine gearbox and further quantified the severity level using various machine learning algorithms [3, 4]. As the acquired vibration signatures are noisy and have non-linear nature, recent studies are more concerned about the implementation of various signal processing algorithms such as wavelet transform, empirical mode decomposition to extract the fault sensitive information from the acquired data [3, 5].
understand the validity of a prognostic estimate, and to characterize model performance over different operating regimes, fault modes, or systems. Performance metrics for monitoring, faultdetection, and diagnostic systems are well established , including accuracy, robustness or auto‐sensitivity, spill‐ over or cross‐sensitivity, fault detectability, uncertainty measures, faultdetection time, and false alarm/missed alarm rates. Appropriate prognostic performance metrics, however, are less understood. Research in prognostic model performance metrics has focused on three areas: algorithm performance, computational speed, and economic incentive metrics. Obviously, it is desirable for prognostic algorithms to make accurate and precise RUL estimates. However, by the very nature of prognostics, these estimates ideally are made in an online fashion, which means the algorithm must have an acceptably short computation time. This is of particular import for systems which intend to have real‐ time data collection and RUL estimation running during system use. Metrics to characterize the computational cost of prognostic algorithms include complexity , specificity , CPU time , and “Big O” runtime notation . It seems reasonable to assume that, given ample funds, the rate of increasing computer speed, and the use of more sophisticated computational methods , a system will be available to make an RUL prediction in any prescribed time frame. Economic metrics, such as Return on Investment (ROI), may consider model performance in making cost benefit analyses [95, 109, 113, 114]. Generally, these analyses show that PHM systems decrease maintenance costs, while increasing availability and improving safety. However, these metrics are primarily intended for a management group and are not considered model performance metrics for this research.
The need of computer systems that are constantly mon- itoring the health status of critical systems, by implement- ing prognostics and healthmanagement (PHM) processes, is particularly important for increasing the reliability while decreasing the maintenance costs . PHM consists of three main processes: faultdetection, diagnostics and prognostics. Faultdetection can be defined as the process of recognizing that a problem has occurred regardless of the root cause . Fault diagnostics is the process of identifying the faults and their causes . Fault prognostics can be defined as the prediction of when a failure might take place . Prognostics has recently attracted significant research interest due to the need of models for accurate RUL prediction for different applications. RUL prediction of critical components is a non trivial task for many reasons. Sensory signals for instance are usually hidden by noise and it is very challenging to process and to extract informative representation of the remainingusefullife . Another problem is the prediction uncertainty due to the variation of the end of life time that can differ for two components made by the same manufacturer and operating under the same conditions. Therefore, proposed models should include such uncertainties and represent them in a probabilistic form .
Another promising and optimized approach for the components replacement is the Condition Based Maintenance (CBM) approach, in which the replacement is based on the real health condition of the aircraft components . Using this strategy, the goal is to monitor the degradation of the different components and predict its future behavior. The health assessment is done through an intelligent analysis of the data retrieved from the different aircraft sensors. For prognostic purposes, the output of the CBM approach corresponds to the RUL of the component being analyzed, which is the number of hours/cycles remaining of usefullife, that is, the remaining time that the component is estimated to be able to function without any fault or anomaly interfering with the nor- mal operation . There are different machine learning methods or techniques used to compute the RUL . Hence, in order to visualize and compare the RUL obtained from different approaches applied over the same dataset, an online tool is proposed. Over the years, different web-based platforms have been developed with the goal of online ex- perimentation, applied in many different contexts .
The MLE-IG method is used to estimate the drift coefficient and the diffusion coefficient offline by utilizing the degradation data of 2#-15# GaAs laser and gives 𝜂̂ = 0.4968 and 𝜎 = 0.1941. Fig. 7 compares the estimated RUL distributions from the offline MLE-IG method with the parallel simulation method at different monitoring time points. The results show that the actual RULs of two methods fall within the range of the estimated RUL distributions at each monitoring point. However, it is observed from Fig. 7 that the PDFs of the estimated RULs for the offline MLE-IG method are typically more dispersed to reflect a stronger uncertainty. Note that the offline MLE-IG method uses the historical data to estimate the drift coefficient and diffusion coefficient and once the estimation is completed, the parameters change no longer. This results in that the effects of individual differences cannot be considered, and the model parameters cannot be evolved by utilizing the real-time monitoring data. The parallel simulation method not only overcomes the effects of Markov property and considers the influence of monitoring noise and drives the WSSM evolution driven by the real-time degradation data. As a result, the comparative results show that the parallel simulation method can effectively reduce the uncertainty of RUL prediction and improve the accuracy of RUL prediction. This further demonstrates that the proposed parallel simulation approach can estimate the RUL with lesser uncertainty and higher accuracy.
Abstract: In this paper, we introduce the Prognostics and HealthManagement of gear bearing system using autoencoder neural networks. Bearings and gears are the most common mechanical components in rotating machines, and their health conditions are of great concern in practice. This study presents an outlier modeling method for forecasting the gear bearing system failure using the health indicators constructed from mechanical signal processing and modeling. Outlier modeling aims to find patterns in data that are significantly different from what is defined as normal. In the unsupervised outlier modeling setting, prior labels about the anomalousness of data points are not available. In such cases, the most common techniques for scoring data points for outlyingness include distance-based methods density-based methods, and linear methods. The conventional outlier modeling methods have been used for a long time to detect anomalous observations in data. However, this paper shows that autoencoders are a very competitive technique compared to other existing methods. The developed method is demonstrated using the IMS bearing data from NASA Acoustics and Vibration Database.
estimates the output uncertainty using a feedforward ANN. Practical applications of PI estimations can be found in (Secchi et al., 2008), where the uncertainty of the estimation of safety parameters is quantified using bootstrapped ANNs; in (Rana et al., 2013), where the Lower Upper Bound Estimation method (Khosravi et al., 2011b) is applied to electricity load prediction for separately estimating the lower and the upper bound of the prediction interval; in (Baraldi et al., 2012), where the PIs of the predicted turbine blade creep growth are estimated; in (Ak et al., 2013), where a ANN is trained to provide the PIs of scale deposition rate in oil & gas equipment; in (Hosen et al., 2015), where an ANN ensemble procedure embedding the Lower Upper Bound Estimation approach and Genetic Algorithm is used to improve the quality of PIs by optimizing the aggregation weights; in (Ak et al., 2015), where an ANN is used for the uncertainty quantification of short-term wind speed prediction. For a comprehensive review of ANN- based PIs, the interested reader can refer to (Khosravi et al., 2011a).
After the selection of degradation indicator, a prediction model should be established to perform the RUL prediction. There are mainly two categories of prediction methods: model-based methods and data-driven methods. An accurate physical model and a correct fault propagation model are essential to a model-based method. Liu and Mahadevan  proposed a unified multiaxial fatigue damage model for rolling contact fatigue, while Xu et al.  developed an improved Paris model to predict residual fatigue life of bearings online. Jin et al.  built a degradation model for lubricant loss in bearing to predict the RUL of an individual momentum wheel bearing. If precise models are obtained, the model-based methods can provide satisfying prediction results. However, due to the complex structure, it is hard to build the physical-based models. In contrast, the data-driven methods are practical and easy to be operated, since they predict the RUL only based on the condition monitoring data. Moreover, the prediction result can be updated with new inspection data available. Yan and Lee  utilized logistic regression to achieve performance degradation assessment. Pham and Yang  developed a liner autoregressive moving average (ARMA) model and a nonlinear generalized autore- gressive conditional heteroscedasticity (GARCH) model to explain the fault condition of machine. Fei and He  applied multiple-kernel relevance vector machine (MkRVM) as an intelligent system to predict the state of bearings. Dong et al.  employed the support vector machine (SVM) to track the degradation process of bearings and utilized Markov model to improve the prediction accuracy. Artificial neural network (ANN) has also been widely used to RUL prediction due to the well performance of function approximation. Tian  proposed an ANN to predict the RUL of pump bearings, with ages and velocity measurements as inputs and the life percentage as output. Wu et al.  and Huang et al.  developed a back-propagation (BP) neural network for estimating the failure time of bearings. Lee et al.  utilized an Elman neural network for health condition prediction. In order to achieve more accurate prediction, Shao and Nezu  applied different neural networks to different running stages of bearings. Gebraeel et al.  proposed two classes of neural network models to perform the RUL prediction, and the result testified the advantages.
Our goal is to provide multi-step ahead prediction of ball bearings health index. One step ahead is to predict the next data using historical data in a fixed window. For multi-step ahead predicting, the first step is predicted by applying one step ahead predicting. Subsequently, the predicted value is included as the latest component of input series to predict the next step using the one step ahead training method. This procedure is repeated for the continuous predicting. The following content briefly describes the basic steps in experimental research. Firstly, raw data set is from the vertical vibration streaming data of PRONOSTIA ball bearings and industrial ball bearing test data. Secondly, health index feature is extracted by Eq. (1). Thirdly, the data format required by the grey neural network framework is reconstructed by using the time window processing technique. Fourthly, the learning set 1 includes AGO health indexes from Bearing 1-1, Bearing 1-2, Bearing 1-3, Bearing 1-4, Bearing 2-1, Bearing 2-2, Bearing 2-3 and Bearing 2-4. The learning set 2 includes AGO health indexes from bearing 6311-1. The test set 1 consists of 8 AGO health indexes: Bearing 1-5, Bearing 1-6, Bearing 1-7, Bearing 2-5, Bearing 2-6 and Bearing 2-7. The test set 2 is AGO health index of bearing 6311-2. The learning set is divided into training set, validation set and test set, and the corresponding allocation ratio is 75 %, 15 %, 15 %. Fifthly, BP, GRNN, Elman and NARX learn on the learning set respectively in order to predict the health index of ball bearings remainingusefullife. Finally, the training model is used to predict the test set. MAE, RMSE, 𝑅 and test running time are used to evaluate the performance of the four neural networks on the test set.
The proposed model for prognosis aims to assess the machine’s performance degradation and foretell the RUL through the use of diagnosis and prognosis in a manner that can take the strengths of each. To apply this method, an online monitoring process is first carried out to acquire the system’s condition. The data obtained from the diagnosis can be properly managed and utilised by the RVM approach for making a prognosis. A flowchart of the combination between diagnosis and prognosis is shown in Figure 2. The suggested method consists of two steps. The role of each one can be summarized as follows. The diagnostic routine starts with data acquisition using multi-sensors attached to the operating system. Then, embossed operating state features are extracted from the collected data (considering root mean square (RMS) as the monitoring indicator). This calculated feature (RMS) will be used to reflect the system’s health and to supervise the level of anomaly using a predefined threshold of diagnosis. Next, an automatic alarm is triggered to prevent machinery performance degradation or malfunction. The alarms triggered in the diagnostic phase are dependent on the quality of feature extraction; the existence of non- robust features may lead to false or missed alarms when the monitoring tool cannot detect the existence of a system fault. The prognosis routine starts when the alarm is activated. After identifying the fault in the diagnosis step, the historical data are employed by calculating the feature. This feature can be used to represent the degradation evolution of the observed system.
The results published for exponential Brownian Motion error exponential process (BM) and exponential stochastic process with Independent Identically Distributed error (IID) model in  are compared with that of the NBC at times equal to 0,5, 0.75 and 0.9 of the bearing failure time T d . The best prediction among BM, IID and NBC for each of the four test bearings is highlighted in bold in Table 3. Note that these do not serve as direct comparisons because the data for training the NBC in this work is a subset, rather than an identical set, of that used for estimating the prior distributions in .
failures. The preventive maintenance strategy consists of age-based, calendar/clock-based, opportunity-based and condition-based. Age-based specifies the age of an asset measuring time in operation such as the number of take-offs and landings for an aircraft, while clock-based maintenance tasks are conducted at specific calendar times; a block replacement policy (Rausand and Høyland, 2004). In the special case, where the downtime due to maintenance and the downtime due to repair/replacement is negligible, the calendar-based and the age-based maintenance policies become alike (Tang, 2012). In practice, clock-based is easier to schedule compared to age-based. The former is less proficient than the latter from random maintenance scheduling before renewal (Tang, 2012). Opportunity maintenance – preventive maintenance applicable for multi-item systems where maintenance tasks on other items give an opportunity for carrying out maintenance, which were not the cause of opportunity (Rausand and Høyland, 2004). Pintelon and Gelders (1992) opine opportunity maintenance replaces equipment components, which are yet to fail based on available maintenance resources. This opportunity maintenance improves system availability and reduce production loss by reducing operations excellence and increases production efficiency (Borges, 2015). Condition-Based describes measurements of one or more condition variables of an asset, which are initiated when a condition variable passes a threshold (Rausand and Høyland, 2004). Rausand and Høyland (2004) state that condition-based is also known predictive maintenance, which determines the state of an in-service system to predict future maintenance when the need arises. The concept assesses the health condition of an equipment continuously and extrapolates to a predefined failure threshold (Camci and Chinnam, 2010; Eker et al, 2011). The condition-based maintenance is one aspect of focus in this research with further discussions presented in the next section.
Among them, the method based on artificial intelligence mainly relies on machine learning, and attempts to understand the trend of equipment degradation from a large number of historical data containing fault labels and process degradation characteristic quantity to achieve residual lifeprediction . However, this method usually requires a sufficient amount of historical failure data as a support, but as the reliability of the equipment continues to increase, it is often difficult to obtain a large amount of failure data or it will spend huge costs. In contrast, the lifeprediction method based on statistical data obtains the probability distribution of the residual life by establishing a mathematical statistical model of equipment performance degradation, which not only predicts the average residual life, but also the impact from uncertainty is taken into account, so it has certain advantages.
In the method of RUL prediction, from the perspective of economic and safety, the method of RUL prediction based on degradation modeling has become the mainstream [17-19]. Literature  systematically and completely reviewed the degradation modeling methods, such as Wiener process, Gamma process, Markov chain and hidden Markov process. However, the existing degradation process described by the Gamma process, Markov chain, and Hidden Markov process basically assumes that the degradation process is monotonous and irreversible. Moreover, in engineering practice, due to the load condition of the equipment, the dynamic change of the internal state, and the change of the external environment, it is possible to accelerate or decelerate the degradation process, that is, the measured performance degradation data has non-monotonic characteristics. The Wiener process has good mathematical properties, and it is suitable for describing non-monotonic random degradation processes with increasing or decreasing trends in engineering practice. At the same time, it can obtain the RUL distribution required by healthmanagement, rather than a single point estimation, so it has been widely applied to degradation modeling and RUL estimation [20-22].
RUL prediction, the entire life cycle bearing data originated from the Center for Intelligent Maintenance Systems  is analyzed. The experimental data sets are collected from run-to-failure bearing test on the designed test platform (Figure 3). Four bearings are installed on a shaft. The rotation speed is kept at 2000 r/min by using an AC motor coupled to the shaft via rub belts. A 6000 lb radial load is applied onto the bearing and shaft by using a spring mechanism. A PCB 353B33 High Sensitivity Quartz ICP Accelerometer was installed on bearing housing. A vibration data sample of 20480 points was collected every 10 minutes by a National Instruments DAQCard-6062E data acquisition card. The sampling rate is set as 20 kHz, the vibration data are recorded on the test bench, and more details can be found in .
Recently, similarity-based approaches have been intro- duced for the RUL estimation problem. In this kind of approaches, test units (whose remaining lives are to be pre- dicted) are matched to the library of training units (available from run-to-failure data) and the most similar instances are used to estimate the RUL. The authors of  have won the 2008 PHM challenge with a similarity based approach that relied on a modified euclidean distance between training and test units. In this method, the whole test trajectory is used to be matched to the library of training units.