Thoughts and Conclusions :: Applications (Neural Network Toolbox)

Neural Network Toolbox

Thoughts and Conclusions

The linear network was able to adapt very quickly to the change in the target signal. The 30 samples required to learn the wave form are very impressive when one considers that in a typical signal processing application, a signal may be sampled at 20 kHz. At such a sampling frequency, 30 samples go by in 1.5 milliseconds.

For example, the adaptive network can be monitored so as to give a warning that its constants are nearing values that would result in instability.

Another use for an adaptive linear model is suggested by its ability to find a minimum sum-squared error linear estimate of a nonlinear system's behavior. An adaptive linear model is highly accurate as long as the nonlinear system stays near a given operating point. If the nonlinear system moves to a different operating point, the adaptive linear network changes to model it at the new point.

The sampling rate should be high to obtain the linear model of the nonlinear system at its current operating point in the shortest amount of time. However, there is a minimum amount of time that must occur for the network to see enough of the system's behavior to properly model it. To minimize this time, a small amount of noise can be added to the input signals of the nonlinear system. This allows the network to adapt faster as more of the operating points dynamics are expressed in a shorter amount of time. Of course, this noise should be small enough so it does not affect the system's usefulness.

Network Training Appelm1: Amplitude Detection