Review, analysis and synthesis of prognostic-based decision support methods for condition based maintenance

Abstract

In manufacturing enterprises, maintenance is a significant contributor to the total company’s cost. Condition based maintenance (CBM) relies on prognostic models and uses them to support maintenance decisions based on the predicted condition of equipment. Although prognostic-based decision support for CBM is not an extensively explored area, there exist methods which have been developed in order to deal with specific challenges such as the need to cope with real-time information, to predict the health state of equipment and to continuously update maintenance-related recommendations. The current work aims at providing a literature review for prognostic-based decision support methods for CBM. We analyse the literature in order to identify combinations of methods for prognostic-based decision support for CBM, propose a practical technique for selecting suitable combinations of methods and set the guidelines for future research.

Appendix

The current section provides details about background of ID3 algorithm and its logic adapted to the problem examined, that is the synthesis of the combinations of methods existing in literature for prognostic-based decision support in CBM. More specifically, it provides the theoretical background of ID3 algorithm, the notation that we used for the formulation of the problem, the ID3 equations as well as the pseudo-code of the application of the ID3 algorithm for constructing the decision tree.

The ID3 DT algorithm is based on information theory and tries to minimize the number of comparisons among the data of the training set. The core idea behind the algorithm is asking questions the answers of which provide the most information. The splitting criteria are prioritized according to the information gain; splitting criteria with more information gain are used first. The decision tree is constructed by employing a top-down, greedy search through the given sets to test each attribute at every tree node. Information is measured by the entropy which represents the amount of uncertainty of a data set D (Chen et al. 2014). Based on the entropy, the information gain can be measured. Information gain is the difference in entropy from before to after the data set D is split on an attribute A or equally, how much uncertainty in the data set was reduced after splitting it on an attribute A (Gaddam et al. 2007; Jin et al. 2009).

Next, we apply the ID3 algorithm by using the following notation:

• X is a set of feature vectors, also called feature space.

• C is a set of classes.

• D is an input dataset

• c: Ideal DT classifier

The main goal of ID3 is to construct (based on D) a decision tree T to approximate c: X -$>$ C, where c is the ideal classifier for X (Adhatrao et al. 2013). In our case, the method classification problem is formulated in the ID3 notation as follows:

• X: the four criteria-attributes (desired output, available input, domain knowledge as utility function, knowledge of the degradation process) with all possible values

• C: Labels of methods (e.g. BN-MDP)—Several research works may use the same combination of methods

• D: Combinations of methods derived from the literature review (see Table 3)

• c: The resulting DT

As it has been already mentioned, information entropy represents the amount of uncertainty of a given data set D and can be expressed as:

$$\begin{aligned} H\left( D \right) =-\sum \nolimits _{x\in X} p\left( x \right) log _2 p\left( x \right) \end{aligned}$$

(1)

where $p\left( x \right)$ is the percentage of the number of elements in class $\hbox {x}_{i}$ to the number of elements in data set D.

Equation 1 is used for calculating entropy in each remaining attribute. The attribute with the lowest entropy is needed for splitting the data set D in each iteration. The classification in the other attributes, which have higher entropy, can be improved (Adhatrao et al. 2013).

Calculation of entropy is needed in order to calculate the information gain, which is defined as the difference in entropy after splitting a data set on an attribute comparing to the entropy before splitting (Sathyadevan and Nair 2015). So, information gain can be expressed as:

$$\begin{aligned} IG\left( {D,X} \right) =H\left( D \right) -\sum \nolimits _{s\in S} p\left( s \right) H\left( s \right) \end{aligned}$$

(2)

where S is the set of subsets that are created after splitting the data set.

The pseudo-code of the application of the ID3 algorithm for the classification of the combinations of methods according to the four criteria is shown below (adapted from (Jin et al. 2009) and (Kietz et al. 2009)):