Prognostics: a literature review
- 5.2k Downloads
Integrated systems health management (ISHM) is an enabling technology used to preserve safe and reliable operation of complex engineering systems. It also helps in reducing processing and operation time, manpower and cost, and increasing system availability and utility. ISHM includes various technologies ranging from design, analysis, build, and verify to operate and maintain. Prognostics is one of the most challenging and beneficial aspects of ISHM. Knowledge of the remaining useful life using prognostics can make a significant paradigm shift in ISHM. Researchers that have new interest in prognostics need to read hundreds of articles to have a complete picture about prognostics and its relation to other disciplines. Our contribution to solving this problem is by introducing the first comprehensive vision about prognostics as a part of ISHM in a single literature review paper. We focus on prognostics benefits, approaches, applications, and challenges. This paper can be considered as the starting point for studying prognostics and health management.
KeywordsCondition-based maintenance (CBM ) Integrated systems health management (ISHM ) Prognostics Prognostics and health management (PHM ) Proactive maintenance
Air Force Research Laboratory
Assembly integration and testing
Artificial neural networks
Adaptive neural fuzzy inference system
Center of Advanced Life Cycle Engineering
Cumulative relative accuracy
Dynamically linked ellipsoidal basis function
Department of Defense
Evolutionary multiobjective optimization
End of life
End of useful prediction
Gaussian process regression
Integrated systems health management
Integrated Vehicle health management
Joint strike fighter
Line replaceable units
Multiobjective decision support system
Mean time between failures
Operation and support
Open systems architecture for condition-based maintenance
Prognostics decision support mechanism
prognostics center of excellence
Prognostics and health management
Physics of failure
Printed wired assembly
Return on investment
Real time engine diagnostics-prognostics
Relevance training vectors
Remaining useful life
Relevance vector machine
Strategic Avionics Technology Working Group
Turbine engine diagnostics using artificial neural networks
Total ownership cost
Unified modeling language
United Technology Company
Unit under test
Vehicle management computer
Vehicle operations network
Monitoring and maintenance have been always around. Due to rapid increase in engineering systems complexity, especially transportation vehicles, complete, and integrated system for vehicle fault detection, diagnostics, failure prognostics, maintenance planning, operation decision support, and decision making, was needed and became a huge challenge.
NASA was the first organization interested in ISHM (or IVHM) since the IVHM panel was established by NASA SATWG in 1990.
improving system safety and reliability which increases the probability of mission success;
reducing processing and operation time, manpower, and costs;
increasing system availability and utility
it moves the strategy of maintenance and decision making from being reactive to be proactive ;
secondary damage reduction;
reconfiguration and replaning in case of failure to optimally use the RUL of the failed parts and complete the mission safely ;
maintenance planning, enhancement of logistic support, and alerting the crew about the impending failure;
knowledge of hidden evolving fault (due to normal internal system tear, wear, and degradation) from multidimensional and spars sensors data.
The paper is organized as follows.
Section 3 gives an overview about ISHM and its benefits, and discusses about how the idea of ISHM started and its challenges.
Section 4 talks thoroughly about prognostics and its relation to health management, shows how prognostics has improved and can be applied in several areas, describes different prognostics approaches, advantages and disadvantages of each approach and how multiple approaches can be combined together to produce better results, and finally discusses the prognostics challenges and how to deal with all of these challenges.
Section 5 presents the summary and conclusion.
Integrated systems health management (ISHM)
Due to the complexity in safety critical engineering systems, traditional ways for system operation and maintenance are not efficient. Failure in such systems can be catastrophic and causes loss of lives or at least mission aborts.
To ensure safe and reliable operation, systems must be continuously and fully monitored. Correct and timely decision must be taken at all stages of the system life cycle from design to O&S in an integrated way.
ISHM helps in fault prevention, mitigation and recovery during operation .
Maintainers, logisticians, engineers, safety persons, mission planners and program managers benefit from ISHM . ISHM also helps system designers, developers, and testers to improve their systems using the feedback data about system field operation and behavior.
ISHM has many incomplete definitions. Some of these definitions do not consider design, development, and test stages as a part of ISHM. Others neglect logistics, resources allocation, and the decision-making process. The definition of ISHM must cover all stages of the whole system life cycle. We see ISHM as an integrated process that is applied to the systems, subsystems, and components from its birth as an idea to its EoL to preserve its health and the desired performance and in the same time ensures safety, availability, reliability, and autonomy and minimize cost. This process integrates system design, development, testing, and evaluation with fault detection, fault diagnosis, and failure prognosis as well as decision support and decision making into a comprehensive system that uses all gathered information, operational demands, and available resources to take appropriate decisions about mission planning, resources allocation, required reconfiguration, maintenance strategies, logistic support, and management strategies taking into consideration closing the loop between each consecutive steps as shown in Fig. 1.
Origin and revolution
Interests in ISHM started when the NASA Office of Space Flight identifies IVHM as the highest priority technology for present and future space transportation systems . That is, the concept started and applied only for vehicles and was known as IVHM. As the systems are growing and their complexity are increasing, this concept crossed the transportation vehicles and became preferable for systems and subsystems; then the term changed to be ISHM. To avoid confusion, the two terms IVHM and ISHM are applicable.
In November 1989, NASA Strategic Transportation Avionics Technology Symposium was held, and then in 1990 the SATWG was established. SATWG initiated some activities and formed panels to fulfill these activities. One of these panels was the IVHM panel which focuses on IVHM planning and NASA/industry interaction. IVHM held several meetings and then definition of IVHM requirements; determination of NASA, DOD, and industry desires, needs and capabilities; and determination of IVHM technology needs, goals, and objectives were significantly built up .
OSA-CBM  is an implementation of ISO-13374. ISO-13372  defines terms relating to condition monitoring and diagnostics of machines. ISO-17359  sets out guidelines for the general procedures to be considered when setting up a condition monitoring program for machines. These standards are part of a huge series of condition monitoring and diagnostics of machines standards.
NASA Ames Research Center and the Jet Propulsion Laboratory are playing a huge rule in ISHM systems development. The United States DoD forces project managers to consider diagnostic, prognostic, system health management, and automatic identification technologies .
The aviation safety program.
The agency roles and responsibilities for NASA.
The 2007 national plan for aeronautics research and development-related infrastructure.
The 2007 next-generation air transportation system research and development plan.
Nevertheless, many ISHM programs have been initiated, but few of them could be considered as a complete and perfect example. This is due to the gap between health management user objectives and engineering development .
In an unprecedented step to increase understanding and deliver higher level of ISHM professionals, Cranfield University offered Master of Science in IVHM .
A lot of efforts have been exerted in ISHM to obtain mature and widespread systems. Additional efforts need to be undertaken to enable widespread adoption of ISHM and resolve its challenges.
Developing tools and techniques that combine messages from single aircraft health management system and results from analysis of fleet-wide health management system into an integrated real-time automated reasoning and decision-making system.
Avoiding system/component malfunctions and failures because of the difficulties in detecting, diagnosing, and mitigating hardware faults and failures in-flight with the existing technologies. These failures can imply catastrophic accidents.
Deployment of the ISHM system due to the big difference between ISHM user objectives and engineering development.
Ability to quantify exactly the benefits of the newly developed ISHM.
Difficulties to provide aviation systems with effective ISHM system.
Resolving tasks of aging and expected life and cost vs. benefit.
Prognostics is one of the top ten challenges in NASA aviation safety program. It plays the most important role in improving system safety, reliability, and availability.
Prognostics itself is not a new concept, since humans are anxious about what will happen in the future to either avoid catastrophes or at least cope with it. Also in business, the coal miner used to put canaries into the mine to know in advance the level of oxygen: it is bad if the canary dies. Prognostics played a historical rule in medicine and is considered as a matured technology that has its special impact on patient management tasks . On the other hand, prognostics is still a developing technology in engineering.
guarantee safe operation to EoL;
output multiple RULs due to different failure modes;
combine RULs with an uncertainty index to be trusted.
historical normal and faulty operational data;
current and future scenarios (operating and environmental conditions, maintenance actions);
manufacturing data, e.g., failure modes effect and criticality analysis and material conditions and variations.
minimization of machines downtime and better productivity ;
moving from fail and fix strategy to predict and prevent ;
reduction of inventory due to the knowledge beforehand about the time to failure; this knowledge allows planners to order only the needed spare parts when required;
total life cycle cost management optimization due to improvement of CBM using prognostics ;
unseen degradation detected and projected from system-monitored parameters.
Prognostics and health management (PHM)
Prognostics itself is useful because it supplies the decision maker with early warning about the expected time to system/subsystem/component failure and let him decide about appropriate actions to deal with this failure. The benefit from prognostics can be flourished if its information is used as the main source to system health management. PHM is the emerging engineering discipline that links studies of failure mechanisms to system life cycle management .
PHM can also change the strategy in the system design and development by achieving high system reliability without adding many redundant devices. High reliability is achieved by replacing static reliability of the system calculated in design phase by online dynamic reliability calculation in actual operating conditions.
The main objective of creating the PHM system is to maximize ROI by combining different maintenance strategies (e.g., scheduled maintenance, condition-based maintenance, and predictive maintenance) to achieve optimum cost-effectiveness versus performance decisions .
PHM is quickly evolving because many organizations have started recognizing the benefits of applying the PHM systems. Rolls-Royce has a long history in applying PHM concepts in aeronautics, especially in engines health management . The BAE systems established a project for fleet health monitoring and machine learning technology for CBM and applied this system to heavy duty transit bus to enable fleet health management remotely in different cities .
The Xerox Company found that embedded and remote PHM can be the key to achieve customer satisfaction with minimum overhead due to after sale service . General Electric developed a PHM project for aircraft turbine engines that are already in service . This project focuses on satisfying user needs by applying all PHM aspects (sense, diagnostics, prognostics, and decision making) to already in service engines resulting in reduction in system O&S cost, reduction, or elimination of maintenance tasks, improvement of mission planning, and enhancement of prognostics capability. UTC and Pratt and Whitney created a generalized PHM value model to identify different values to customers and providers and correlate these values to concrete metrics .
The F-35 JSF aircraft is a complete and comprehensive example of applying PHM concepts. PHM for JSF is the key enabler for its AL support . AL allows reduction in logistics footprint, safety improvement, increase sortie generation rate, and reduction in O&S cost. PHM allows fault detection and isolation in real time onboard the aircraft for all main systems and subsystems. It also allows failure prognostics for a selected critical systems and components. Recommended actions are also displayed for pilot when needed to avoid the predicted failure. The PHM capability for JSF aircraft is the main reason for using single engine aircraft with high reliability as dual engines.
Prognostics approaches are classified in different ways. Sometimes, the classification is based on the type of available data and knowledge about the system. Another time prognostics approaches are classified according to the type of the used methodology. The prognostics system developers can benefit from these classifications in algorithm selection based on available background about the system and suitable forecasting techniques. Prognostics approaches classification also helps in identifying what techniques from other technologies can be used in prognostics algorithms development. A key point about prognostics approaches classification is building a way to obtain a standard methodology for prognostics applications development within a standard framework.
reliability based approach;
The advantages of this approach dwells in its simplicity and can be easily applied. It does not require any knowledge about failure modes or system operation. Although the simplicity of this method, it has many drawbacks. The main problem about replacing a part at every fixed interval is that the component-specific conditions are not considered causing either early replacement of working component or late replacement that implies component failure before replacement. It is also hard and inaccurate to apply this approach to newly developed components, because it requires massive failure historical data.
PoF-based prognostics is one of the major methodologies used for prognostics. It is located on the top of the pyramid of prognostics approaches Fig. 9. In this approach, a physical model for the system or component is developed. This physical model is a mathematical representation of failure modes and degradation phenomenon. To establish this model, a thorough understanding of the system/component physics is required. In addition to knowledge about the system, knowledge about operating conditions and life cycle loads applied to the system/component are also required.
Modeling of the system can be at a micro level, i.e., modeling the effect of stresses into the material by establishing for example a finite element model. Another level of modeling is to establish a macro-level model. A macro-level model is based on the first principle knowledge about the system to model the relation between its component parts. Modeling is performed by mathematical equations such as modeling degradation of turbofan engines as a function of efficiency loss and flow .
After establishing the system model, an in situ monitoring of the system is performed, then system diagnosis is used to assess its performance. The model can use the knowledge about the current system health and future scenario about the load exposure to forecast RUL. Figure 11 shows a description of PoF methodology for prognostics .
Physics-based prognostics has been applied to the systems in which their degradation phenomenon can be mathematically modeled such as in gearbox prognostic module , residual-based failure prognostic in dynamic systems (applied to hydraulic system) , and military LRU prognostics .
There are some drawbacks and limitations of this approach that hold it back from being widely spread such as: developing a high fidelity model for RUL estimation is very costly, time consuming, and computationally intensive and sometimes it could not be obtained. Also, if this expensive model is obtained, it will be component/system specific and its reusability will be very limited to other similar cases. For all of these reasons, sometimes the next approach (data-driven) is used instead of the physics-based one.
Data-driven prognostics approach is the recommended technique when the feasibility study implies a difficulty of obtaining a PoF degradation model. Although the physics-based approach is preferable because of its accuracy, precision, and real-time performance, the data-driven prognostics is more widely spread than the physics-based one in the PHM community. This wealth of available applications based on data-driven prognostics is due to its quick implementation and deployment. Data-driven approach mainly relies on techniques from AI which has its readymade tools that could be applied directly with minor modifications. The low cost of algorithms development and no or little knowledge required about system physics make this approach preferable by prognostics system developers.
The idea about this approach is to use the measured performance parameters of the system, e.g., pressure, temperature, speed, vibration, current ..., etc. to create a model that correlates these parameters variation to system degradation and fault progression and then use this model for RUL estimation. The creation of this model is solely based on techniques from soft computing, e.g., ANN, fuzzy logic, neuro-fuzzy, support vector machine, RVM ..., etc., and sometimes techniques from statistics such as regression analysis. Techniques from soft computing are preferable than statistics because of their ability for noise rejection and learning hidden relations between parameters. Data-driven techniques can be classified into conventional numerical methods and machine learning methods Fig. 12.
The key requirement for data-driven prognostics algorithm development is the availability of multivariate historical data about system behavior. These data must cover all phases of system normal and faulty operation as well as degradation scenarios under certain operating condition. Availability of these data for algorithm training is a challenging task, but once the data are available, the creation of the algorithm will not be a matter.
Three methods can be used to obtain run to failure data for prognostics algorithm development: (1) fielded applications; (2) experimental test beds; (3) computer simulations . Fielded applications suffer from that the systems continuously monitored rarely fail, whereas failed systems do not have sufficient sensors. In the same time when data are available, proprietary issues pan these data to be available for public use. Experimental test beds are costly, dangerous, and time consuming. Accelerated aging may not contain all failure modes. Computer simulation is complex and difficult, because building a high-fidelity simulation model is not an easy task, but once this model is available, computer simulation can be considered the best way to acquire run to failure data . PCoE at intelligent system divisions in NASA Ames research center provides a huge data repository for prognostics algorithm development that is available for public use .
Data-driven methodology is mainly used at systems and subsystems level that experience gradual degradation. These systems/subsystems are equipped with multiple sensors that can monitor its operating behavior.
There are two ways for RUL estimation using data-driven approach: either to use the developed model of system behavior to directly calculate the remaining useful system life or to use this model for system health state estimation and then extrapolate or project the system health to obtain the degradation curve until it intersects with the failure threshold to calculate RUL .
Of course, these steps are not mandatory because sometimes the situation changes from one system to another, but it can be used as a guideline for prognostics system developers. In some cases, diagnostics system could not catch the starting of system degradation, because the degradation phenomenon could not be monitored. This happens when the degradation is due to internal system wears and tears and it is too difficult to have direct sensor readings of its deviation from normal values. In this case, using AI techniques to learn the relation between monitored parameters and system health is the best solution. Many tools from the data mining community can be used to discover the hidden relationships between the monitored parameters to explain the strange behavior of system degradation.
Usage of data-driven prognostics has many advantages such as no system knowledge is required, it is fast and easy to implement, the algorithm can be tuned to be used for another system, and hidden relations about the system behavior may be learned.
A lot of prognostics applications are based on the data-driven methodology. The very famous data-driven solutions are presented in the 2008 PHM conference (PHM08) data challenge competition where training and test data are provided for unknown complex engineering systems. The objective was to estimate RUL for this system in the test data where no information about system physics or even system type was provided. It was a pure data-driven problem. Heimes  used recurrent neural network trained by extended Kalman filter to solve this problem. Wang, Yu, Siegel, and Lee  used similarity-based prognostics to tackle the PHM08 problem. The wining algorithm for this competition used Kalman filter ensemble of multilayer perceptron neural networks for RUL estimation .
Usage of multivariate and noisy data requires a robust algorithm.
Because most of the techniques are based on approximation, uncertainty management must be taken into consideration which is another challenge.
Sometimes, the results are not intuitive because of the absence of physical knowledge about the system.
It can be computationally intensive due to large datasets that affect the real-time performance. Well-designed algorithm and suitable resources can overcome this problem, but it remains a challenge in development.
Overfitting and overgeneralization while training the algorithm can affect the results tremendously.
There is unavailability of data, especially for newly developed systems.
Zio and Di Maio  developed a similarity-based algorithms for online identification of failure modes and RUL estimation of nuclear systems. The computational performance analysis of the proposed methodology showed its applicability for online application. However, the algorithm is tested on an Intel® Core2 Duo of 1.83 GHz that exists in normal personal computers and not vehicles onboard computers.
Hu et al.  proposed an ensemble of multiple data-driven algorithms to achieve a performance better than each individual algorithm. This method is efficient because it is not limited to the proposed algorithms, but allows addition of any other data-driven algorithm.
It could be a good solution to combine both physics-based and data-driven methodologies into one hybrid approach to gain the benefits from each and overcome its limitation.
As mentioned above, each technique, either PoF or data driven, has some limitations. A hybrid (or fusion) approach is combining both data-driven and PoF approaches together to get the best from each, i.e., PoF can compensate the lack of data and data driven compensates the lack of knowledge about system physics. This fusion can be performed either before RUL estimation which is called pre-estimate where PoF and data driven are fused to perform RUL estimation or after RUL estimation by fusing the results from each individual approach to obtain the final RUL called post-estimate .
Cheng and Pecht  presented a case study for RUL estimation using fusion approach for ceramic capacitors. Another application based on this approach is the prognostics of lithium ion battery . Goebel et al.  used a fusion approach for aircraft engines bearing, and the results show that this method gives more accurate and robust outcome than using either data driven or PoF alone.
Although this approach is used to eliminate the drawbacks of PoF and data-driven methods and gain their benefits, it also carries the disadvantages of both methods to a certain extent, but of course not by the same level if each technique is used individually.
The Kalman filter which is adaptive in nature and particle filter are used for the implementation of this methodology.
In the last few years, great attention has been given to prognostics due to its good effect in improving complex engineering systems health management.
Prognostics has a great contribution in different fields such as in medicine where the future course and outcome of the disease processes are predicted after treatment  and in everyday weather forecast. Medicine and weather forecast are mature prognostics applications that already proved its applicability. We are here concerned about prognostics applications in engineering fields which is still an Achilles’ heel in CBM and needs to be matured enough as in medicine and weather forecast.
Prognostics applications can be online and works in real time or near real time whether it is onboard or off-board. Prognostics also can be applied off-line regardless of the operation time of the monitored system. The real-time prognostics takes online data from the data acquisition system to perform RUL estimation and gives a warning about the impending failure to allow system reconfiguration and mission replaning. The off-line prognostics system uses fleet wide system data and performs deep data mining processes that could not be performed onboard in real time due to the lack of resources and time criticality. The results from off-line prognostics system can be used in maintenance planning and decision making for logistics support management.
Applying prognostics in the engineering field is not easy because system’s EoL must be forecasted accurately in sufficient time in advance to allow the controller to react and prevent system failure. In this section, we demonstrate some of the prognostics applications in different engineering fields.
Vehicles prognostics applications
As long as safety is one of the most important aspects that prognostics is created for, many prognostics applications are directed towards safety critical parts of vehicles especially in aerospace.
One of the most important prognostics system has been developed for EMA which plays a dominant rule in controlling surfaces of new-generation fly-by-wire aircraft and spacecraft in severe conditions [53, 54]. EMA is a safety critical part. The ability to confidently monitor, diagnose, and prognose EMA can save lives as well as millions of dollars. NASA Ames Diagnostic & Prognostic Group in collaboration with Impact, Moog, Georgia Institute of Technology, California Polytechnic State University, Oregon State University, and US Army developed a very useful PHM system for EMA. The developed system can be used onboard in real time to provide current and predicted EMA health that allows safe reconfiguration. To achieve this goal, a flyable electromechanical actuator test stand is developed and used in laboratory experiments as well as in flight onboard UH-60 Blackhawk aircraft. After the diagnostics system catches the fault, the prognostics system which uses GPR is initiated for RUL estimation based on the fault mode and intersection of fault progression with the fault threshold. Results show that prediction error of time to failure is less than 10 %.
Aircraft gas turbine engine is a safety critical system that needs to be health monitored and proactively maintained. Due to the complexity of such a system, creation of physical model for system prognostics is very difficult and costly. ANN can identify faulty and nominal system behavior if it is trained appropriately. It also has the ability of novelty detection, but needs massive training data and looks like a black box. Data mining rule extraction tools can also perform the same task and give more insight into the behavior than ANN.
Brotherton et al.  used a combination between ANN and rule based for development of online aircraft prognostics system to take the benefits from both techniques. This combination is based on an algorithm called TREPAN Fig. 18. The idea about this system is to use DL-EBF neural networks to learn system nominal and faulty state as well as stages of fault progression. The benefit of using DL-EBF is that it gives more insight into the system dynamics. The rule extraction module data mines the neural network by queries to generate the rules used for trending. The good things about this system is that it does not require massive data for training, especially at the beginning of fault evolution, good statistical performance, discovery of new rules, novelty detection, and real-time performance.
Pacific Northwest National Laboratory did a feasibility study for development of embedded real-time prognostics system for gas turbine engine AGT1500 used on the M1 Abrams tank . This work is sponsored by the US Army Logistics Integration Agency for evaluating the ROI from prognostics technology. The system is developed as an ad hoc for already manufactured engines. It uses 25 sensors originally installed by the manufacturer and 13 other sensors are added for the purpose of system development. Additional data acquisition system is used for sensors readings collection and processing. A microprocessor(s) is used for data analysis and EoL prediction. This system is called REDI-PRO and is an extension of TEDANN. RUL estimation is done using regression analysis. Results showed that the benefit of the prognostics system is its cost of about 11:1 which prooves the applicability of prognostics in such effective areas.
Prognostics plays a dominant rules in industry to increase system availability and utility.
Using logistic regression to build a model that maps performance parameters to the probability of failure.
Real-time system performance is evaluated by inputting online data on the model.
RUL estimation is obtained by using autoregressive moving average and the prediction is dynamically updated with time.
Electronics are very important and are used widely in complex systems such as aircraft and spacecraft. The failure of such electronics can lead to a failure of the whole system. Electronics used in such complex systems are always exposed to thermal cycle loads that affect its operation. The development of embedded diagnostics and prognostics system that runs onboard in real time with low power and cost is a challenge.
Rouet et al.  presented PWA as a case study of embedded diagnostics and prognostics system for electronics. The system is implemented using a data logger of the type Lifetime Assessment Monitoring System. Data are collected by in situ smart sensors and then prediction is made using the PoF technique (Fig. 20). The results are evaluated by comparing the output from the algorithm to the results from accelerated tests performed on the PWAs. Results showed very low discrepancies between the real experiment measurements and the model output which ensures the applicability of this method.
Tuchband and Pecht  used prognostics for military LRU exposed to severe flight conditions. The use of prognostics was a part of complete interactive supply chain for the US military. The LRU is monitored online by an embedded sensor. Sensor data are transferred remotely to the base station using a wireless communication. After data analysis, the result of this analysis is uploaded to a Web portal for RUL estimation. Integration of wireless communication, Web portals, and prognostics allows not only RUL estimation, but also availability of this data for multiple users worldwide.
Recent years have seen a rapidly growing interest in research on Li-ion battery health monitoring and prognostics with a focus on battery capacity estimation and RUL estimation. Saha and Goebel  found a base for health management application for energy storage devices by presenting an empirical model to describe battery behavior during individual discharge cycles and over its cycle life. This model is used further for RUL estimation.
Wang et al.  introduced a novel methodology for Li-ion battery prognostics. This methodology is based on RVM to find the RTVs. Then RTVs are used to calculate the parameters of the conditional three-parameter capacity degradation model using least square regression. Finally, the RUL is obtained by extrapolating the fitted model to reach the failure threshold.
Hu et al.  proposed a multiscale framework with extended Kalman filter for state of charge and capacity estimation. Then Hu et al.  extended this work and used Gauss–Hermite particle filter to project the capacity fade and calculate the RUL with high accuracy and uncertainty representation of the estimate.
Hu et al.  proposed a data-driven methodology for estimating the capacity of Li-ion battery based on the charge voltage and current curves. In this methodology, five characteristic features of the charge curves are defined to indicate the capacity. Then a regression model based on k-nearest neighbor is developed to identify the relation between the five features and the capacity. Particle swarm optimization is used to find the optimum weight combination of the five features. This data-driven methodology was verified and accurately estimated the capacity of Li-ion battery.
Onboard resources used to run prognostics algorithm are always a barrier for the deployment of prognostics solutions. To resolve this challenge, Saha et al.  developed a distributed prognostics algorithm using GPR. All computer nodes run diagnostics routines, once an off-nominal situation is detected, and nodes running prognostics module related to the fault mode engages in RUL estimation. Wireless communication between nodes is used which imposes more difficulty to the system. A case study for battery health management is conducted to prove the concept. Distributed prognostics algorithm can be considered as a large step forward in prognostics algorithm development.
All of the discussed prognostics applications were just examples, whereas the prognostics applications could not be counted. Prognostics is widely used and applied in several engineering areas such as unmanned aerial vehicle propulsion, military aircraft turbofan oil systems, semiconductor manufacturing, cracks in rotating machinery, heating, air conditioning, wheeled mobile robots, electronics, gas turbines, actuators, aerospace structures, aircraft engines, clutch systems, batteries, bearings, and hydraulic pumps and motors. Prognostics is also involved in many projects related to the nuclear industry due to its criticality, e.g., nuclear plant life prediction NULIFE . As the prognostics technology is improving, in the near future it will be part of almost all systems, from the very complex ones to household equipment.
autonomic control reconfiguration based on prognostics output;
integration of different and sparse data collected from interconnected subsystems to be processed;
prognostics system validation and verification;
Here, we will discuss the following major challenges: uncertainty management, validation and verifications, prognostics standardization, and post-prognostics reasoning.
Prognostics in nature is an uncertain process, because it incorporates projection of damage progression into future.
Future loads and environmental conditions used in prognostics cannot be accurately predicted. Besides, there are several parameters imposing uncertainty on prognostics. These parameters exist in the whole system life cycle from design to operation and support.
Assumptions during system design and development, AIT equipment and tools, system model, system inputs, disturbances, data processing, sensors, state estimation techniques, RUL estimation approaches, performance metrics ..., etc. are of course imperfect and participate in uncertainty growth.
Present state uncertainty which is the result from sensor noise, gain and bias, data processing, filtering, and estimation techniques.
Future uncertainty that appears due to loading, environmental, and operating conditions.
Modeling uncertainty: as its name indicates, it comes from all kinds of models used in the prognostics process, e.g., system model and failure model.
Prediction method uncertainty.
Uncertainty in prognostics cannot be eliminated completely, instead it can be managed by noise modeling, algorithm overfitting avoidance, model training, and using hybrid forecasting techniques.
In practice, the error in the RUL estimation is not normally distributed, and sometimes parametric distribution is not even known. When the distribution is not normal, it is better to use median instead of mean to represent the location of the estimation and interquartile range instead of variance to measure the spread. Visualization of data can be done using error bars and box plots Fig. 23.
Saxena et al.  laid a very good and efficient concept for incorporating uncertainty. Instead of using single point estimate and measuring the difference between the estimated EoL and actual EoL, an error bound is presented which is called \(\alpha \)-bounds (Fig. 24). This \(\alpha \)-bound does not have to be symmetric especially in prognostics, which prefers early prediction than late prediction. By integration of the area under the PDF curve from \(\alpha \)- to \(\alpha \)+ and comparing the result to predefined threshold \(\beta ,\) we can know if the prediction is within \(\alpha \)-bounds or not and is called the \(\beta \)-criterion. The parameter \(\beta \) is defined to establish a relationship between uncertainty and risk tolerance of the system.
RUL estimation is so important to the ISHM decision-making process. The amount of uncertainty in RUL estimation informs the decision maker about the percentage of how much he/she can rely on prognostics system results. For this reason, researchers in the past few years identified the RUL estimation task as an uncertainty propagation problem . Sankararaman and Goebel  and Sankararaman et al.  proposed analytical methods such as the most probable point concept and first-order reliability methods to propagate different sources of uncertainty to RUL estimation. These analytical methods are not computationally expensive as sampling methods, which make it useful for online applications. Also, the results from these methods do not change on repetition.
Although the trend of solving RUL estimation problem as an uncertainty propagation task is useful, it focuses only on mathematical methods and neglects the usage of AI techniques which are commonly used in prognostics.
Validation and verification
Validation and verification of the prognostics process is highly required, because deployment of the prognostics system could not be done before the assurance of its performance. Developing a good prognostics algorithm without the ability to quantify its performance makes it useless.
They help in the creation and evaluation of requirement specification needed for system design Fig. 25.
They assess which part of the prognostics system affects its performance that helps in performance improvement.
They can be used in comparison between different algorithms in a standardized way .
They are also used to identify the week areas in prognostics that requires more researches.
Performance metrics are used to identify ROI which is a very important aspect that defines whether to deploy the prognostics system or not .
Since the beginning of applying prognostics concept, focus was only on prognostics algorithms development. Recently, the ISHM community paid too much attention to the importance of having prognostics metrics.
Prognostics performance metrics can be classified as follows:
Functional classification It can be considered as the most important and widely used classification. It is based on the information that the metrics provides to fulfill certain functions Fig. 26.
End user-based classification This classification is based on customer requirements. Each one sees the benefits of the prognostics system from different points of view that need to be quantified by specific metrics. This classification is shown in Table 1.
Performance of prognostics algorithm should improve with time as more data become available. Prediction at the beginning of life is normally less confident than the prediction just before failure. A good algorithm should give a confident prediction with suitable time in advance and the prediction confidence should evolve with time.
That is why prognostics metrics should be dynamic and take into consideration the changing of algorithm performance with time. Saxena et al.  presented four sequential prognostics specific metrics that evaluate prognostics performance and consider the effect of time scale into the performance evaluation.
End user based classification (adapted from )
Economic value of prognostics system
Cost–benefit metrics that relates prognostics performance to cost savings
Resource allocation and mission replaning
Accuracy and precision-based metrics for RUL estimation of the specific unit based on the damage accumulation model
Take appropriate action during the mission and reconfigure operations in case of any contingency
Accuracy and precision-based metrics for RUL estimation of the specific unit based on the fault growth model
Apply proactive maintenance to increase the reliability and availability
Accuracy and precision-based metrics for RUL estimation based on the damage accumulation model
Design and develop the prognostics system based on the user requirements and take feedback from the metrics to improve the future design
Reliability-based metrics to evaluate the design and computational metrics for resource estimation
If the algorithm meets the PH horizon requirements, we can apply the second metric, \(\alpha -\lambda \) Performance. This metric checks whether the algorithm stays within the required accuracy margin (\(\alpha \)-bounds) at a specified time t. As the algorithm approaches EoL, the required accuracy margin at a specific time instance shrinks, which means that the algorithm performance must improves with time as more data become available to be the best just before the EoL. The \(\alpha -\lambda \) performance metric creates an accuracy cone that converges with time (Fig. 29).
The previously discussed metrics are very useful and can be considered as an achievement in establishment of prognostics specific performance metrics. Some other problems still need to be resolved, such as the connection between top-level user requirements and performance metrics. Also, the previously discussed metrics can be used for off-line prognostics algorithm evaluation, so there is a need for online prognostics algorithm evaluation where the ground truth data are not available. Accurate and applicable prognostics performance metrics are needed to obtain a standardized methodology for algorithms validation, verification, certification, and to compare between different algorithms efficiently.
Prognostics standardization is highly required to allow easy, fast, and effective prognostics system development and deployment. It will also unify the concepts within the community and help in identifying technology gaps that need more attention.
Prognostics standardization can be divided into three types: standardization in prognostics terms and definitions, standardization in prognostics system development, and standardization in prognostics metrics.
Standardization in prognostics terms and definitions is intended to remove ambiguity when using different terminologies. This will help clear understanding while reading and discussing any prognostics topic.
ISO-13372 and ISO-13381-1  presents some of these terms and vocabularies. Prognostics national framework  contains a rich glossary of prognostics terms like RUL, UUT, EoL..., etc. as well as definitions like time index, time of detection of fault, prognostics features .... etc.
Standardization in prognostics system development is aimed at generalizing the prognostics process, information exchange within prognostics system, implementation of prognostics system, and prognostics system design methodology. Because prognostics is the key enabler of CBM, the standardization of prognostics system development is identified within the CBM system development.
ISO-13381-1 correlates prognostics process with monitoring and decision-making processes within the e-maintenance architecture (Fig. 32).
Formalization of the prognosis process environment. This is achieved by defining the relation between prognostics process and other business processes such as monitoring, diagnostics, and decision support. It also defines the connections between processes.
Formalization of the prognosis final purpose. The general method is defined for calculating the final output of prognostics which is the RUL. This is performed by defining two things: the first is the threshold of the component performance (usually its EoL); the second is the functional threshold of the whole system performance which defines the limits of the safe and useful system operation.
Formalization of the functional decomposition of the prognosis. For RUL calculation, the prognostics process is divided into four sub-processes: three of them are in sequence to compute RUL (“To initialize state and performances”, “To project” and “To compute RUL”) and the fourth one (“To pilot prognosis”) coordinates the work of the three other sub-processes.
Formalization of the coordination of the sub-processes needed to fulfill the prognosis mission. This is achieved by creating a sequence diagram of the prognostics.
Formalization of the prognosis objects and data. Classes diagrams are presented for prognosis data and objects based on the OSA-CBM standards . This presentation is created using UML classes diagram representation.
Another type of prognostics standardization is the unification of research objectives. This unification is not yet considered by the research community, although it will help to fill the gaps in prognostics technology and create an integrated effort to resolve prognostics challenges.
Post prognostics reasoning
The prognostics system provides one of the information pieces (RUL with the corresponding confidence level) that the decision maker uses with other pieces of information to take appropriate decision about system maintenance and operation to increase system reliability, safety, and availability as well as reduce total life cycle cost and logistics footprint. That is, having valuable information is important but using this valuable information correctly and efficiently is much more important.
Post-prognostics reasoning is a challenge because it requires developing an integrated information system that links the operation, maintenance, logistics, decision support, and decision making, all together in a way that allows each user to benefit from the information that other users have without making any interruption to the system.
ISO-13381-1 defines what to do practically with prognostics information. It identifies the alert (alarm) point for the remaining life before failure of the system that allows taking the required counteraction to rescue system function from failure. Another defined point is the trip (shutdown) limit, at which the system is turned off before failure. Trip limit is normally less than the failure threshold of the system.
The defined limits in ISO-13381-1 do not show the full picture of the post-prognostics reasoning. Iyer, Goebel, and Bonissone  developed a decision support system that uses information from a reliable prognostics system and produces different evaluated decisions to the decision maker to enhance logistics of a fleet of assets. A block diagram of this system is shown in Fig. 33.
The information from the OBPHM is processed in PDSM. PDSM is composed from two modules, the IP and the MODSS. The IP deals with the incoming information and checks its consistency, deals with uncertainty, and aggregates all of these information to be more useful by the MODSS module. The MODSS module contains two submodules the OpSIM module, and the EMOO module. MODSS module provides different ranked decisions and evaluates its impact on the operation. The output from MODSS is presented to the user on an HMI.
More and more implementations of automated decision support systems based on prognostics information are needed to increase the benefit from prognostics system and increase its applicability and acceptance by the engineering community.
Prognostics is quickly evolving, but still needs more attention from governments, industries, and academia to become less of an art and more of a science. This could be done if all efforts in this field are integrated together to obtain a clear and definite steps for prognostics system design, development, validation, and verification.
In this paper, we tried to present a complete vision about prognostics as a major component part of ISHM. We gathered a lot of sparse information about prognostics and combined all of these information together to present an integrated work that shows the importance of prognostics and its influencing rule in ISHM. We also clarified how the maintenance strategies can shift from “fail and fix” to “predict and prevent” based on the proactivity in prognostics and how prognostics is the main building block in CBM. The concept that relates prognostics to health management has been also introduced (PHM). After that, we discussed the prognostics approaches, their advantages and disadvantages, and how to use the suitable technique according to the prognostics problem definition. We also presented a lot of prognostics applications which have been already deployed or are just an experiment. Finally, we addressed the more challenging aspects in prognostics and how the research community is trying to resolve these challenges.
This literature review paper about prognostics is mainly intended for new prognostics researchers. Professional prognostics researchers who delve into the details of different prognostics aspects can also benefit from this paper to recall the concepts.
- 1.Office of Aeronautics and Space Technology (1992) NASA research and technology goals and objectives for integrated vehicle health management (IVHM), Report NASA-CR-192656, 10 Oct 1992Google Scholar
- 2.Schwabacher M, Goebel K (2007) A survey of artificial intelligence for prognostics. In: Proceedings of AAAI fall symposium, Arlington, VA, 9–11 Nov 2007Google Scholar
- 4.Bond L (2008) Diagnostics and prognostics: state of the art and programs. PHM08 tutorial materials, IAEA Workshop, Argentina, 10 Dec 2008Google Scholar
- 5.Wheeler K, Kurtoglu T, Poll S (2010) A survey of health management user objectives in aerospace systems related to diagnostic and prognostic metrics. Int J Prognostic Health Manag 1(1):003Google Scholar
- 6.Saxena A, Balaban E, Goebel K, Saha B, Saha S, Schwabacher M (2008) Metrics for evaluating performance of prognostic techniques. In: International conference on prognostics and health management, Marriott Tech Center Denver CO, 6–9 Oct 2008Google Scholar
- 7.Saxena A, Celaya J, Saha B, Saha S, Goebel K (2010) Metrics for offline evaluation of prognostic performance. Int J Prognostic Health Manag 1(1):001Google Scholar
- 8.Uckun S, Goebel K, Lucas P (2008) Standardizing research methods for prognostics. In: International conference on prognostics and health management, IEEE, Marriott Tech Center Denver, CO, pp 1–10. doi: 10.1109/PHM.2008.4711437. 6–9 Oct 2008
- 10.Feather M, Hicks K, Mackey R, Uckun S (2008) Guiding technology deployment decisions using a quantitative requirements analysis technique. In: IEEE international conference on requirements engineering, Barcelona, Spain, pp 8–12Google Scholar
- 11.Scott N (2011) Introduction to prognostics. In: Tutorial material, annual conference of the PHM society, Montreal, 25–29 Sept 2011Google Scholar
- 12.ISO-13374-1 (2003) Condition monitoring and diagnostics of machines, data processing, communication and presentation, part 1: general guidelinesGoogle Scholar
- 13.OSA-CBM Primer, MIMOSA (2006) Open systems architecture for condition-based maintenanceGoogle Scholar
- 14.ISO-13372 (2004) Condition monitoring and diagnostics of machines vocabulary, 1 st editionGoogle Scholar
- 15.ISO-17359 (2003) Condition monitoring and diagnostics of machines: general guidelinesGoogle Scholar
- 16.Office of the secretary of defense, Mandatory Procedures for Major Defense Acquisition Programs (MDAPS) and Major Automated Information System (MAIS) acquisition programs, DoD 5000.2-R, 5 April 2002Google Scholar
- 17.Aeronautics Research Mission Directorate (ARMD) (2009) NASA, automated detection, diagnosis, prognosis to enable mitigation of adverse events during flight, IVHM technical plan, Version 2.03, 2 Nov 2009Google Scholar
- 18.Derriso M (2012) AFRL integrated systems health management architecture. Air Force Research Laboratory, Tutorial material, 10 April 2012Google Scholar
- 19.Derriso M (2012) AFRL’s integrated systems health management roadmap. Air Force Research Laboratory AFRL, 10 April 2012Google Scholar
- 20.Cranfield University (2011) MSc integrated vehicle health managementGoogle Scholar
- 21.Biswas G, Manders E (2006) Integrated systems health management to achieve autonomy in complex systems. In: Proceedings of 6th IFAC symposium on fault detection supervision and safety for technical processes, BeijingGoogle Scholar
- 24.Byington C, Roemer M, Galie T (2002) Prognostic enhancements to diagnostic systems for improved condition-based maintenance. In: IEEE aerospace conference proceedings, Big Sky, Montana, 9–16 March 2002Google Scholar
- 25.Pecht M, Kumar S (2008) Data analysis approach for system reliability, diagnostics and prognostics. In: Pan pacific microelectronics symposium, Kauai, Hawaii, USA. 22–24 Jan 2008Google Scholar
- 26.Stark D (2010) Prognostics and health management (PHM), tutorial material, international SEMATECH manufacturing initiative, ISMI, July 14 2010Google Scholar
- 27.Bonissone P (2006) Knowledge and time: a framework for soft computing applications in prognostics and health management (PHM). In: International symposium on evolving fuzzy systems, 2006, September, pp 19–24, Ambleside, Cumbria. doi: 10.1109/ISEFS.2006.251159
- 28.Calhoun K (2009) Health management at Rolls-Royce, 2009 Rolls-Royce Corporation, 01 October, 2009. https://www.phmsociety.org/sites/phmsociety.org/files/FieldedSystems_Calhoun.pdf. Last accessed 23 Dec 2015
- 29.Heimes F (2009) Fleet health monitoring and machine learning technology for CBM, BAE Systems. https://www.phmsociety.org/sites/phmsociety.org/files/FieldedSystems_Dresch.pdf. Last accessed 23 Dec 2015
- 30.Hamby E (2009) PHM challenges for a fleet of marking devices embedded in human systems. In: PHM society conference, San Diego, CA, USA, 27 Sept–1 Oct 2009Google Scholar
- 31.Mooney T (2009) Health management for in-service gas turbine engines. In: PHM society conference, San Diego, CA, USA, 27 Sept–1 Oct 2009Google Scholar
- 32.O’Flarity S (2009) PHM experience at UTC and Pratt and Whitney: Challenges and opportunities. In: PHM society conference, San Diego, CA, USA, 1 Oct–27 Sept 2009Google Scholar
- 33.Hess A, Calvello G, Dabney T (2004) PHM a key enabler for the JSF autonomic logistics support concept. In: Proceedings of 2004 IEEE aerospace conference, Big Sky, Montana, USA, vol 6, pp 3543–3550. 6–13 March 2004. doi: 10.1109/AERO.2004.1368171
- 34.Medjahar K, Zerhouni N (2009) Residual-based failure prognostic in dynamic systems. In: 7th IFAC international symposium on fault detection, supervision and safety of technical processes, Sants Hotel, Spain 30 June– 3 July 2009Google Scholar
- 35.Saxena A, Goebel K, Simon D, Eklund N (2008) Damage propagation modeling for aircraft engine run-to-failure simulation. In: International conference on prognostics and health management, Marriott Tech Center Denver, CO, USA, pp 1–9, 6–9 Oct 2008Google Scholar
- 36.Mathew S, Pecht M (2011) Prognostics of systems: approaches and applications. In: Proceedings of the 24th international congress on condition monitoring and diagnostics engineering management, Clarion Hotel Stavanger, Stavanger, Norway, 30 May–June 2011Google Scholar
- 37.Tuchband B, Pecht M (2007) The use of prognostics in military electronic systems. In: Proceedings of the 32nd GOMAC tech conference, Lake Buena Vista, FL, USA, pp 157–160, 19–22 March 2007Google Scholar
- 38.Saxena A (2008) Simulating degradation data for prognostic algorithm development NASA Ames Research Center. https://c3.nasa.gov/dashlink/resources/14/. Last accessed 23 Dec 2015
- 39.Celaya J, Wysocki P, Goebel K (2009) IGBT accelerated aging sata set, NASA Ames prognostics data repository. NASA Ames Research Center, Moffett Field, CA, USA. http://ti.arc.nasa.gov/tech/dash/pcoe/prognostic-data-repository/. Last accessed 23 Dec 2015
- 40.Goebel K, Saha B, Saxena A (2008) A comparison of three data-driven techniques for prognostics. In: Proceedings of the 62nd meeting of the society for machinery failure prevention technology (MFPT), Virginia Beach, VA, USA, pp 119–131, 6–8 May 2008Google Scholar
- 41.Heimes F (2008) Recurrent neural networks for remaining useful life estimation. In: International conference on prognostics and health management, Marriott Tech Center Denver, CO, USA 6–9 Oct 2008. doi: 10.1109/PHM.2008.4711422
- 42.Wang T, Yu J, Siegel D, Lee J (2008) A similarity-based prognostics approach for remaining useful life estimation of engineered systems. In: International conference on prognostics and health management, Marriott Tech Center Denver, CO, USA, 6–9 Oct 2008. doi: 10.1109/PHM.2008.4711421
- 43.Peel L (2008) Data driven prognostics using a kalman filter ensemble of neural network models. In: International conference on prognostics and health management, Marriott Tech Center Denver, CO, USA, 6–9 Oct 2008. doi: 10.1109/PHM.2008.4711423
- 47.Goebel K (2007) Prognostics and health management. Guest lecture, ENME 808A University of MarylandGoogle Scholar
- 48.Cheng S, Pecht M (2009) A fusion prognostics method for remaining useful life prediction of electronic products. In: 5th Annual IEEE conference on automation science and engineering, Bangalore, Karnataka, India, pp 102–107, 22–25 Aug 2009. doi: 10.1109/COASE.2009.5234098
- 50.Goebel K, Eklund N, Bonanni P (2006) Fusing competing prediction algorithms for prognostics. In: Proceedings of 2006 IEEE aerospace conference, Big Sky, MT, USA, 4–11 March 2006. doi: 10.1109/AERO.2006.1656116
- 51.Abu-Hanna A, Lucas P (2001) Prognostic models in medicine AI and statistical approaches. Methods Inf Med 40(1):1–5Google Scholar
- 52.Smith B (2011) Satellite enabled vehicle prognostic and diagnostic system, United States patent application publication US 2011/0046842 Al, 24 Feb 2011Google Scholar
- 54.Balaban E, Saxena A, Narasimhan S, Roychoudhury I, Goebel K (2011) Experimental validation of a prognostic health management system for electromechanical actuators. In: American institute of aeronautics and astronautics AIAAGoogle Scholar
- 55.Brotherton T, Jahns G, Jacobs J, Wroblewski D (2000) Prognosis of faults in gas turbine engines. In: Proceedings of 2000 IEEE Aerospace conference, 2000, vol 6, pp 163–171. doi: 10.1109/AERO.2000.877892
- 56.Greitzer F, Pawlowski R (2002) Embedded prognostics health monitoring. In: International instrumentation symposium, health monitoring workshop, May 2002Google Scholar
- 57.Bonissone P, Goebel K (2002) When will it break? A hybrid soft computing model to predict time-to-break margins in paper machines. In: Proceedings of SPIE 47th annual meeting, international symposium on optical science and technology, Seattle, Washington, USA, vol 4787, pp 53–64Google Scholar
- 58.Rouet V, Delye A, Vichare N, Pecht M, Foucher B (2007) Embedded remaining life prognostics and diagnostics of electronics. In: 1st International CONGRES on microreliability and nanoreliability in key technology applications (MicroNanoReliability Congress), Berlin (D), Germany, 2–5 Sept 2007Google Scholar
- 59.Saha B, Goebel K (2009) Modeling Li-ion battery capacity depletion in a particle filtering framework. In: Proceedings of annual conference of the PHM society, San Diego, CA, 27 Sept–1 Oct 2009Google Scholar
- 64.Saha S, Saha B, Saxena K, Goebel K (2010) Distributed prognostic health management with Gaussian process regression. In: IEEE aerospace conference, Big Sky. MT, USA, 6–13 March 2010. doi: 10.1109/AERO.2010.5446841
- 65.Vachtsevanos G (2003) Condition based maintenance of critical machinery assets: an intelligent architecture. University of Texas, Workshop on automated machinery maintenance, Arlington, TX, USAGoogle Scholar
- 66.Saxena A, Roychoudhury I, Celaya J, Saha S, Saha B, Goebel K (2015) Requirements specifications for prognostics: an overview. In: American institute of aeronautics and astronautics AIAA. https://c3.nasa.gov/dashlink/resources/824/. Last accessed 24 Dec 2015
- 67.Sankararaman S, Goebel K (2015) Uncertainty in prognostics and systems health management. Int J Prognostic Health Manag 6(010)Google Scholar
- 68.Khawaja T, Vachtsevanos G, Wu B (2005) Reasoning about uncertainty in prognosis: a confidence prediction neural network approach. In: Annual meeting of the North American fuzzy information processing society NAFIPS, MI, USA, pp 7–12, 26–28 June 2005. doi: 10.1109/NAFIPS.2005.1548498
- 69.Sankararaman S, Goebel K (2013) Remaining useful life estimation in prognostics: an uncertainty propagation problem. In: Proceedings of the 2013 AIAA infotechaerospace conference, co-located with the AIAA aerospace sciences—flight sciences and information systems event, Boston, MA, USA 19–22 Aug 2013Google Scholar
- 70.Sankararaman S, Goebel K (2013) A novel computational methodology for uncertainty quantification in prognostics using the most probable point concept. In: Proceedings of 2013 annual conference of the prognostics and health management, New Orleans, LA, USA, vol 4 (049), 14–17 Oct 2013Google Scholar
- 72.ISO 13381-1:2004(E) (2004) Condition monitoring and diagnostics of machines—Prognostics, 1st editionGoogle Scholar
- 73.Iyer N, Goebel K, Bonissone P (2006) Framework for post-prognosticdecision support. In: Proceedings of 2006 IEEE aerospace conference, Big Sky, MT, USA, 4–11 March 2006. doi: 10.1109/AERO.2006.1656108
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.