Knowledge-based Models

In the absence of an accurate mathematical model for a complex system with prior principles, the knowledge-based models (KbM) requiring no physical model appear to be promising in real-world applications (Peng et al., 2010).

Knowledge (or experience) based prognostics are simple and easy to perform applications where the historical failure information of systems are available for RUL prediction (George et al., 2006). They evaluate the similarity between an observed phenomena and a library of previously defined failures and deduce RUL expectancy from previous events (Sikorska et al., 2011). Table 2.3 shows the major applications of KbM in prognostics.

Table 2.3: Knowledge Based Models

Merits Limitations

Expert Systems(Butler, 1996; Biagetti and Sciubba, 2004): algorithms mimicking the human expert to solve problems

Effective on particular domains where there is sufficient informa- tion available

Unfavourable in novel cases where there in not sufficient knowledge

Fuzzy Logics (Feng et al., 1998; Satish and Sarma, 2005; Dmitry and Dmitry, 2004): a form of multivalued logic system

Applicable for imprecise data Needs rule definition for complex

cases

Similarity-based Predictions (Wang et al., 2008; Wang, 2010; Eker et al., 2014; Lam et al., 2014; Ramasso, 2014a,b; Bektas et al., 2017): Based on the pairwise distance evaluation defined on two degradation trajectories

High prediction accuracy and ability to reduce prognostic risks

Requires multiple run-to-failure data to estimate RUL

A typical example of KbM is the expert systems (ES) which can be defined as an automated representation of a computer system that is pro- grammed to exhibit how a human expert solves a particular domain problem (Liao and K¨ottig, 2014; Peng et al., 2010). They are based on the rules ex- pressed in the form of ‘IF-THEN” statements acquired from collections of real experiments (Sikorska et al., 2011). These rules can be either heuristic rules or specific domain rules, and they can be chained together using logical operators (Garga et al., 2001). As an example, Butler (1996) introduced an ES for incipi- ent failure detection and predictive maintenance system to assess the integrity

of a power distribution system component and predict the maintenance re- quirements. Their system includes an expert system engine, a knowledge base model, mathematical and network models of equipment ageing and historical readings. Biagetti and Sciubba (2004) also designed an ES based prognostic and intelligent monitoring expert system that can produce real-time informa- tion about the existence of faults, estimate future time for detected and likely faults, and provide suggestions on problem controlling. However, there is no RUL information provided with their method.

Although the outputs of ES methods are comprehensible and reasoning can be evaluated with respect to a particular result, it is not always practical to acquire domain knowledge and convert it to rules, especially when novel sit- uations are not covered explicitly or the system complexity increases (Zaidan, 2014)

Similar to ES, fuzzy logic (FL) is a problem-solving model that provides a simple way to arrive at a definite conclusion based upon imprecise inputs (Peng et al., 2010). A fuzzy system consists of a knowledge base variables to provide intuitive and human-like representation and reasoning with incomplete information. One of the earliest applications of FL in KbM prognostics was used in a chemical pulp mill for incident prevention and real-time process condition monitoring (Feng et al., 1998), and extended into prognostics of bearing faults in induction motors (Satish and Sarma, 2005). Dmitry and Dmitry (2004) also developed such a FL process. Their model maps inputs into fuzzy variables (fuzzification) and uses functions to de-map these variables into numerically precise outputs (defuzzification). Majidian and Saidi (2007) conducted a comparison of FL with a data-driven prognostic model for RUL prediction of boiler tubes and suggested that data-driven model performed better where its applicability is favourable compared to FL model.

inaccurate input information and/or no mathematical model is available to implement; however, it greatly depends on the availability of an expert to define the rules underlying system behaviour and design the fuzzy sets to present each variables characteristics (Zaidan, 2014; Sikorska et al., 2011). The challenges of FL implementation becomes more apparent in the case that experts require to define the rules for a complex system which potentially includes numerous interrelating components.

An alternative KbM is similarity-based prognostics. Despite this ap- proach is categorised under data-driven models by several studies (Liao and K¨ottig, 2014; Eker et al., 2014; Mosallam et al., 2016), it follows the character- istics of KbMs such as similarity evaluation between monitored cases and using the library of degradation patterns for RUL estimations. However, similarity- based prognostics do not model the experience of a domain expert.

Wang et al. (2008) introduced the use of a similarity-based approach for RUL estimation for the International Conference on Prognostics and Health management data challenge, and received the leading score in the competition. Their systematic method includes the calculation of a health indicator for each unit and using the library of degradation patterns from the training units. The approach is particularly suitable for cases where a sufficient number of complete run-to-failure operational data is accessible. Trajectories from multiple units of the same system are used in a collaborative manner to create a library of degradation patterns. In order to predict the remaining lifetimes of the test units, the filtered degradation patterns for the test trajectories are matched to the pre-filtered training patterns in the library. The pairwise distance between pairs of training and test patterns is used to find the best matching position. The actual remaining life of those matched units is then used as the basis for estimation. The distance can be expressed as the average Euclidean distance over multiple trajectories between full degradation models

(training trajectories, q) and a test instance (test trajectory,p). distancei = v u u t l X i=1 (qi−pi)2 (2.17)

Use of similarity based prognostics was extended by Wang (2010); Eker et al. (2014); Lam et al. (2014); Ramasso (2014a,b); Bektas et al. (2017) into RUL prediction of complex systems. The proposed algorithms are shown to be very effective in performing RUL prediction but they require a systematised data-processing method. Therefore, the above-mentioned similarity-based al- gorithms are used along with data-driven approaches for data processing.