process fault and homoclinic explosion in the lorenz system

This paper deals with the problem of process faults in the lorenz system that can affect any of the system parameters and cause the system to exhibit various behaviors. in this paper, the homoclinic orbits in the lorenz system are described and then the occurrence of process faults in the system is investigated that can cause a homoclinic explosion, bifurcation, change of fixed point, or even instability in the system. in such systems, where a small change in one of the parameters causes large changes in the behavior of the system, to prevent disaster in industrial systems and also to stop the propagation of faults in the system, the faults must be identified as soon as possible. in this paper, the states in the system are estimated by using a reduced-order observer, and the faults are detected. the purpose of this article is to recognize the change in behavior of this system in the face of this type of fault and to express the importance of timely detection and identification of faults in the system so as not to lead to failure and disaster in industrial systems. finally, the effect of process fault, disturbance, and sensor fault are investigated simultaneously and the states and faults in the system are estimated.