Adaptive weighting input estimation of a nonlinear system

Figures & data

Figure 1. The NEE of the estimated harmonic force F(t) = sin(3t) vs fading factor for the air-damped isolator model using CIE.

Figure 2. The normalized estimated errors of the three estimated shocks vs fading factor for the air-damped isolator model using CIE.

Figure 3. The harmonic force F(t) = sin(3t) estimation of the air-damped isolator model. (a) AWIE method, (b) CIE method (γ = 0.1) and (c) CIE method (γ = 0.9).

Figure 4. The half-sine wave shock estimation of the air-damped isolator model. (a) AWIE method, (b) CIE method (γ = 0.1) and (c) CIE method (γ = 0.9) (force unit, kg m ms⁻²).

Figure 5. The rectangular shock estimation of the air-damped isolator model. (a) AWIE method, (b) CIE method (γ = 0.1) and (c) CIE method (γ = 0.9) (force unit, kg m ms⁻²).

Figure 6. The triangular shock estimation of the air-damped isolator model. (a) AWIE method, (b) CIE method (γ = 0.1) and (c) CIE method (γ = 0.9) (force unit, kg m ms⁻²).

Figure 7. The consecutive loads of different magnitudes estimation of the air-damped isolator model. (a) AWIE method, (b) CIE method (γ = 0.1) and (c) CIE method (γ = 0.9) (force unit, kg m ms⁻²).

Table 1. The NEE of the estimated harmonic force F(t) = sin(3t).

NEE	CIE (%)	AWIE (%)
γ = 0.1	1.5	1.2
γ = 0.9	41.9

Table 2. The relative errors of the peak-to-peak values of the estimated harmonic force F(t) = sin(3t).

Relative errors	CIE (%)	AWIE (%)
γ = 0.1	1.1	1.3
γ = 0.9	29.8

Table 3. The NEE of the three estimated shocks.

Type of shock	NEE (%)
	CIE		AWIE
	γ = 0.1	γ = 0.9
Half-sine wave	0.5	3.3	0.4
Rectangular	5.5	9.3	5.4
Triangular	0.3	5.5	0.2

Table 4. The relative errors of the estimated maximum amplitudes of the three estimated shocks.

Type of shock	Relative errors (%)
	CIE		AWIE
	γ = 0.1	γ = 0.9
Half-sine wave	1.1	2.5	0.9
Rectangular	2.0	0.4	1.9
Triangular	2.0	19.2	1.9