By utilizing the IGHS, the identification diagram of nonlinear discrete-time systems based on the pruned second-order Volterra model is shown in Figure 1.
The goal of the IGHS is to find the optimal kernel vector H for Volterra filter model so that the difference between the estimated output y[n] and the actual system output [?
By using the IGHS to optimize MSE, we can obtain the most appropriate kernel vector for the second-order Volterra model.
To verify the validity of the IGHS on identifying nonlinear system based on second-order Volterra filter model, two examples including the highly nonlinear discrete-time rational system and the real heat exchanger are considered.
In this experiment, the IGHS is used for Example 1awith N = 5.
In addition, the minimal mean square error (MSE) obtained by the IGHS is equal to 5.
Additionally, the minimal MSE yielded by the IGHS is equal to 3.
For Example 1b with N = 5 and N = 8, the IGHS parameters are the same as those for Example 1a, and Figures 4 and 5 display the comparisons of results for Example 1b with N = 5 and N = 8.
Moreover, the IGHS parameters used for Example 2 are the same as those of Example 1.
According to the results, we can see that the IGHS performs better most of the time.
Additionally, Mann-Whitney U test [27, 28], also known as "Mann-Whitney Wilcoxon test," is used to ensure a statistical significant difference between the IGHS and any of the other three HSs.
In order to compare the IGHS with the other three HSs in a statistical way, three groups of Mann-Whitney U tests are executed, and they are ([U.