The increasing complexity of mechanical systems has resulted in an increased usage and dependence on data driven modelling techniques in order to obtain simple yet accurate models of these systems. Neural networks have emerged as a popular modelling choice due to their proven ability to learn complex nonlinear relationships between inputs and outputs of any given system. Moreover, they are capable of generalizing on data that they have not been trained on. The downside of modelling with neural networks is that they do not provide any insight into the dynamics of the system they model. This limits the application of neural networks in carrying out fault diagnosis of mechanical systems to just the fault detection and isolation (FDI) tasks. While in some applications this may be sufficient, sometimes alongside FDI, it is also desirable to carry out a fault identification task in order to determine the necessary adjustments to bring the faulty system back to its normal operating condition. This thesis explores the possibility of carrying out a fault identification task alongside an FDI task for a mechanical system that has been modelled by a neural network. Traditionally, the weights of a trained neural network represent the strength of a connection between the two neurons they connect. The possibility of an existing correlation between the weights of a neural network and the properties of the mechanical system being modelled is a concept that has not been fully explored yet. This study considers that such a relation exists, implying that the change in certain properties of the mechanical system due to the occurrence of a fault can be related to a change in the corresponding weights of the neural network modelling the system. Consequently, the change in weights of the neural network could give an insight into the fault occurrence in a mechanical system. Taking this idea forward, two fault diagnosis algorithms have been proposed in this study - a fault detection algorithm using adaptive threshold, and a fault isolation & identification algorithm based on sparse Bayesian learning framework. The proposed algorithms were tested on (hypothetical) faulty linear and non-linear systems. The results show that the adaptive threshold based fault detection algorithm was successful in detecting the occurrence of faults in the linear system. For the non-linear system, although a simplistic neural network was used to model the system, the fault detection algorithm was still successful while returning few and sparse false positives and negatives. The fault isolation & identification algorithm was also successful in isolating and identifying all the changed weights in the neural networks modelling the system for both linear and non-linear cases. Although the algorithms proposed show promising results for the experiments conducted, further research is needed to establish the suitability of using them in real world applications.