Empirical Gramian-based spatial basis functions for model reduction of nonlinear distributed parameter systems

Figures & data

Figure 1. The model reduction framework of the combined spatial basis functions.

Figure 2. The measured time evolution of distributed temperature of catalytic rod for testing.

Figure 3. The roots of mean square error based on spectral basis functions and two kinds of new spatial basis functions for spatio-temporal evolution of catalytic rod temperature.

Figure 4. The first three new spatial basis functions by balanced truncation method for model reduction of Equation (23).

Figure 5. The first three combined basis functions by balancing of empirical Gramians for model reduction of Equation (23).

Figure 6. The distributed error based on three new spatial basis functions by balanced truncation method for model reduction of Equation (23).

Figure 7. The distributed error based on three combined basis functions by balancing of empirical Gramians for model reduction of Equation (23).

Figure 8. The No. 4 random temporal input of the Chaffee–Infante equation.

Figure 9. The measured spatio-temporal output of Chaffee–Infante equation for testing.

Figure 10. Roots of mean square error based on spectral basis functions and two kinds of new spatial basis functions for model reduction of Chaffee–Infante equation.

Figure 11. The first two new spatial basis functions by balanced truncation method for model reduction of Chaffee–Infante equation.

Figure 12. The first two combined spatial basis functions by balancing of empirical Gramians for model reduction of Chaffee–Infante equation.

Figure 13. The approximated error based on two new spatial basis functions by balanced truncation method for model reduction of Chaffee–Infante equation.

Figure 14. The distributed error based on two combined spatial basis functions by balancing of empirical Gramians for model reduction of Chaffee–Infante equation.