This paper presents a technique to improve the accuracy of the predictions obtained using the Rough Set Theory (RST) in non-deterministic cases (rough cases). The RST is here applied to the data collected by the Intelligent Field Devices for identifying predictive diagnostic algorithms for machinery, plants, subsystems, or components. The data analysis starts from a historical data set recorded from the field instruments, and its final result is a set of “if–then” rules identifying predictive maintenance functions. These functions may be used to predict if a component is going to fail or not in the next future. The prediction is obtained by applying the rules extracted with the RST algorithm on the real-time values transmitted by the field device. It may happen that some diagnoses are uncertain, in the sense that it is not possible to take a certain decision (device sound or close to fail) with a given set of data. In this paper, a new algorithm for increasing the confidence in these uncertain cases is presented. To show an example, the proposed confirmation algorithm is applied to the predictive algorithms obtained for an intelligent pressure transmitter.
The Rough Set Theory (RST) has great potentialities in the area of predictive maintenance. RST is one of the mathematical techniques for extracting automatically information hidden in a database (KDD = knowledge discovery in database). KDD is commonly defined (Fayyad et al., 1996 and Piatetsky-Shapiro and Frawley, 1991) as “the non-trivial process of identifying valid, novel, potentially useful and ultimately understandable patterns in data”.
Thus the KDD process starts from the atomic pieces of information (data) and processes them to obtain information at a higher-level (knowledge) and to present them in an organize form (pattern).
KDD is based on multiple successive actions, such as: selection, pre-processing, transformation, data-mining, and interpretation. The very core of KDD is the data-mining ( Hand, Mannila, & Smyth, 2001) that represents a mathematical tool to find unsuspected relationships between data, and to summarize the data in novel ways that are both understandable and useful to the data owner. Several techniques for data-mining exist, and the paper focuses on the RST that seems to be promising for defining predictive maintenance algorithms.
The RST technique is quite robust and results obtained in the medical field, where the theory was first applied, are quite good. The idea behind RST is to cross-correlate non-homogenous data to find-out the data that are most significant for predicting the system health. It seems to be possible to use the RST for obtaining diagnostic algorithms for industrial plants or subsystems, machinery, and Intelligent Field Devices (IFD) as well. IFD are devices (transmitters, actuators, inverters, and so on) with a digital core, and the capacity of transmitting large quantities of additional data together with their basic information. These data can be used to evaluate the system operational status and to predict future failures or collapses. Applying the RST to a historical database containing records of symptoms (internal parameters) and operational status (sound, abnormal, failed), it is possible to create a predictive tool to be used with the real-time data flow. Rules extracted from the RST are in the form “If–Then”, therefore very simple to implement in a control system even with limited computational power. The obtained rules can be written in a script file, that has a very small size and that can be executed using very small CPU and memory resources. This means that even the CPU of an IFD can run such scripts without installing specific software or mathematical tools. Thus the diagnostic algorithms can be directly executed on board without using the control system resources. The “If–then” rules correlate directly the data existing in the IFD, without the need of adding external parameters or variables (i.e., the weights in a neural network).
An important feature of RST is its capacity of shrinking the size of the database, since it considers only the data really useful for finding out the diagnosis. In fact, some records of the database may be redundant, and some of the features may not be useful for determining the value of the decision attribute. RST is very effective in eliminating these redundant data.
This paper presents in the first part the fundaments of the RST technique, with a particular focus on the management of uncertain cases, called rough concepts. In the framework of RST, uncertainty means that two or more database items having the same symptoms present different diagnosis.
The second part of the paper defines a new algorithm based on the cluster analysis for increasing the confidence about the diagnosis of uncertain cases. The aim of this algorithm is to compute the probability associated with each possible diagnosis for every rough concept. We call it a confirmation algorithm.
At the end of the paper a practical case is studied. The RST and the proposed confirmation algorithm are applied to an intelligent pressure transmitter. A model for the predictive diagnostic is presented and discussed.
Rough Set Theory is used in the paper to identify diagnostic algorithms for implementing predictive maintenance functions for industrial plants, subsystems, machinery, and intelligent field devices. Starting from a set of historical data, RST allows defining straightforward maintenance functions in the form of if–then rules. The paper presents a new confirmation algorithm to increase the confidence in the diagnosis for uncertain cases.
The algorithm is based on the calculation of a weighted distance of elements pertaining to the boundary set (that is with uncertain decision) from the centers of the clusters of elements with certain decision. This distance is assumed as an index of the probability that an uncertain element pertains to one of the two certain partitions of the universe. The distance is used together with the probability calculated with the conventional RST techniques to assign a decision to uncertain elements.
The application of this confirmation algorithm to a set of rules extracted from a database of intelligent pressure transmitters seems to give satisfactory results.
