When an advanced mechanical system fails, there is often a degraded process from weak fault to failure. It is often accompanied by a series of engineering phenomena. These subtle engineering phenomena are the responses of different mathematical dynamics models on complex mechanical systems. Due to the complexity of mechanical systems, these mathematical models are often nonlinear and time-varying. Therefore, researchers need to use advanced evolution equations and numerical analysis methods to accurately characterize the performance parameters of the mechanical system at different stages, and establish the dynamic mathematical model of the mechanical system at different times.
By these mathematical models, researchers indirectly analyze the failure of the mechanical system and predict the remaining life of the mechanical system to maximize the production and manufacturing of the company.