## 1 Introduction  
The Artificial Neural Networks (ANNs) [1; 2] have an established position among the data-driven techniques which are applied to identify non-linear dynamic systems [3]. It follows from the fact that such computational approach can be used when a knowledge about the system in the form of physical description is not available. Thanks to learning capabilities, in a relatively easy way without large effort of work a neural model of quite complicated system may be obtained. Moreover, generalisation properties of the ANNs allow to use such a model in several practical applications for different data sets not used during system identification. The above mentioned properties and especially the ability of modeling of complex non-linear dynamic systems cause that the ANNs stand out among the Fault Diagnosis (FD) methods within the analytical/model-based approaches, signal-based approaches, knowledge-based approaches can be distinguished [4; 5; 6; 7; 8; 9; 10]. To the task of the FD methods belong the fault detection, isolation and identification [9; 11] but the fault detection seems to be essentially crucial because it determines appropriate performing of the fault isolation and identification. Commonly the fault detection relies on the comparison of the diagnosed system with its nominal model [11; 12]. Unfortunately, the efficacy of such method strongly depends on the quality of neural model. Therefore, all kinds of efforts to its improvement should be made. In practice the researchers usually only focus on the problem of the proper neural model architecture selection or/and training algorithms improvements [2; 3; 13]. However, it is worth noting that very rarely the problem of appropriate data selection in the context of the ANN quality improvement is taken into consideration. Moreover, assuming that the model is rarely an ideal copy of the diagnosed system in the nominal fault-free state what often results from the measurement noise included in the data used during system identification, the mathematical description of its uncertainty [8] should be delivered. The omission of such factors as the model uncertainty, measurements noise and other disturbances during FD may lead to undetected faults or false alarms what is not accepted in the modern industrial systems. In other words, the robust FD system against such factors should be designed. To calculate the uncertainty of the ANN the class of the Outer Bounding Ellipsoid (OBE) algorithms [14; 15; 16; 17] can be used. There is of course a wide spectrum of approaches which can be used to asses model quality in various contexts [18; 19; 20; 21]. However, the aim of this paper is to obtain a model with possibly small output variance, which is associated with the so-called D-optimality criteria [22; 23]. As a result the aim is to minimize the volume of the model parameters uncertainty region. In this paper the proposed modification of one of such algorithms can be applied to training the Multi-Layer Perceptron (MLP) [1; 2; 3] and alongside calculating its uncertainty as the feasible parameter set. Moreover, a new approach for the MLP quality improvement with the application of the Sequential D-optimum Experimental Design (SDED) is proposed. All that efforts are going to propose a new robust and efficient adaptive threshold-based Robust Fault Detection (RFD) system. In particular, it is composed of three main stages:  
1. It is based on the classical approach to training neural networks and can be realized with state-of-the-art approaches available in the literature;
2. Having, an initial structure and parameters of a neural network a novel Modified Nonlinear Quasi-OBE Algorithm (MNQOA) with optimal input sequence is used to gradually decrease its uncertainty. After this process, an adaptive threshold is obtained for the resulting neural network. 3. The neural network obtained in Stage 2 along with an associated adaptive threshold are used for the on-line RFD.