Criteria for determining the optimal levels of multilevel perturbation signals for nonlinear system identification

A method is developed for determining the optimal levels of multilevel perturbation signals for nonlinear system identification, using the condition number of matrices derived from a Vandermonde matrix of the set of signal levels. It is applicable to the identification of nonlinear systems when the perturbation signal is applied directly to static nonlinearity. The optimal signal level sets of size q obtained when the order of the nonlinearity is q - 1 are virtually identical to those obtained previously for Volterra series models by a more complex method. With the new method, optimal signal level sets can also be obtained for every order of nonlinearity less than q - 1, in most of which the number of different signal levels is less than the signal level set size q. The results indicate that, for nonlinear system identification, a confidence limit is reached when 7 levels signals are used for the identification of 6-th order nonlinearities. They also show that, for the identification of an r-th order nonlinearity, there is little point in using signals with more than r + 1 different levels, although in most cases the size of the optimal signal level set that contains these levels will be greater than r + 1. The method gives optimal signal level set that are independent of the number of occurrences of the signal level set during a measurement period. Their values are shown to be the global optima for pseudo-random perturbation signals derived form maximum length sequences, in which the zero level occurs one time less than the other levels during a period. For periods of 100 or more, the differences between the actual and global optima are less than 1%.