Mathematical models of technical constructions are favourably designed by the method of finite elements. They can be improved by methods of identification. By use of these mathematical models, it is possible to design state observers, which estimate the complete physical state of the systems by using only measurements at a few available points in combination with the mathematical model. In structural mechanics observers can be applied to monitor vibrations, to ascertain the maximal stress and to calculate the life of the system. They can also be used to supervise characteristic parameters of the structure such as eigenfrequencies.
The application of observers for large systems might cause problems. This is mainly due to the high number of degrees of freedom within the mathematical model. A solution is provided using "modal observers", developed by modal analysis. These observers have turned out to be very efficient. Usually it is sufficient to observe only a few low eigenfrequenties. In this way even complicated structures can be observed in real time. An intelligent monitoring of machines or buildings becomes possible. The control of mechanical structures can be also simplified and improved by the use of modal observers.