## 2 Related Works: Active and Passive Approaches to Fault Detection  
As it was already mentioned, the main objective of this paper is to develop a technique which makes it possible to enhance performance of a neural network-based fault detection scheme. Before proceeding to the subsequent deliberations, let us start with precisely defining fault diagnosis process which is composed of three phases [9]:  
**fault detection:**: it makes it possible to undertake a diagnostic decision concerning the fault. In other words, it provides a binary decision concerning the fault, e.g., a pump is faulty;
**fault isolation:**: it enables to determine the location of the fault, e.g., an induction motor driving the pump is faulty;
**fault estimation:**: it allows to determine the size of the fault as well as its time varying nature, e.g., the induction motor driving the pump is faulty and it locts 20% of its performance.  
The objective of the remaining part of this section is to review fault detection detection strategies which can be divided into two classes [24; 25; 26; 27; 28]:  
**Active fault detection:**: aims at eliminating modeling uncertainty;
**Passive fault detection:**: focuses on providing a adaptive threshold forming an enclosure associated with modeling uncertainty.  
Let us start with the active approaches, which can be generally divided into observer-based [18; 29; 30] and parity relation ones [28; 31; 32]. In both cases, modeling uncertainty is represented by the so-called unknown input which is suitably decoupled during the fault detection procedure. Apart from their incontestable appeal, active approaches have one common disadvantage, which is associated with the fact that along with decoupling unknown inputs, there is a chance that the faults can be decoupled as well. Thus, their design requires suitable caution preventing such an unappealing effect. Even if the unappealing full fault decoupling is avoided, there is still a chance of reduced fault sensitivity. Alternative approaches are named as passive ones. Instead of decoupling model uncertainty, they aim at providing its enclosure in which all responses of fault-free system should be contained. The first attempt at developing such an approach was made by [PERSON] et al. in 1988 [33]. The authors clearly indicated that performance of all fault detection systems is influenced by modeling uncertainty. They presented a unique framework incorporating a knowledge of modeling error in the analysis and design of fault detection systems. The developed framework was called threshold selector and it evolved in the subsequent literature to adaptive threshold [34; 35]. Irrespective of the name being used, the optimal threshold is shown to be a function of the bound on modeling errors as well as the noise properties. Such a bound is frequently called uncertainty interval [32; 36; 37] and it is a natural fact that it should be as small as possible to provide reliable diagnostic decisions. The concept of passive fault detection was developed for various classes of systems and applications, e.g., power converters, motor systems, intelligent autonomous vehicle, wind turbines, oil and gas industry.  
In the light of the above discussion, the objective of this paper is to propose a neural network-based fault detection scheme and then to enhance its performance by minimizing the size of the uncertainty interval. For that purpose a quality measure called Mean Uncertainty Interval (MUI) [38; 39; 40] is employed. Finally, it should be noted that the proposed approach does not estimate the fault but it provides a binary evaluation if there is the fault or not. Thus, fault convergence analysis can be investigated during the last phase of fault diagnosis which is fault estimation. This is, however, beyond the scope of this paper and it is indicated as a future research direction.