Two-sided bounds on the mean vector and covariance matrix in linear stochastically excited vibration systems with application of the differential calculus of norms

Figures & data

Figure 1. Multi-mass vibration model.

Figure 2. Curve $y=\Vert P_x{(t)-P\Vert }_2,0\le t\le 25,\mathrm{\Delta }t=0.1$.

Figure 3. Right norm derivative $y=D_{+}{\Vert P_x(t)-P\Vert }_2,0\le t\le 25,\mathrm{\Delta }t=0.1$.

Figure 4. Second right norm derivative $y=D_{+}^2{\Vert P_x(t)-P\Vert }_2,0\le t\le 25,\mathrm{\Delta }t=0.1$.

Figure 5. $y=\Vert P_x{(t)-P\Vert }_2$ along with the best upper and lower bounds.