Distributed design for active fault diagnosis

Figures & data

Figure 1. The decomposition of an LSS into interconnected subsystems.

Figure 2. Scheme of distributed AFD algorithm.

Table 1. Transition probabilities of the models.

	${\mu }_k^1$			${\mu }_k^2$
${\mu }_{k+1}^1$	1	2	${\mu }_{k+1}^2$	1	2
1	0.9	0.1	1	0.9	0.1
2	0.1	0.9	2	0.1	0.9

Table 2. Performance of decentralised and distributed PFD and AFD architectures for Example 5.1.

PFD
Input	est.	$\hat{J}$	$P_{\mathrm{MD}}$	$P_{\mathrm{FA}}$	$T_{\mathrm{on}-\mathrm{line}}$ [s]
Random	DEC	3.731	1.72%	2.08%	0.250
	DIS	3.351	1.73%	1.67%	0.410
Switch	DEC	1.142	0.47%	0.80%	0.251
	DIS	0.707	0.46%	0.30%	0.411
AFD
Design	est.	$\hat{J}$	$P_{\mathrm{MD}}$	$P_{\mathrm{FA}}$	$T_{\mathrm{on}-\mathrm{line}}$ [s]
DEC	DEC	0.303	0.09%	0.16%	0.299
	DIS	0.271	0.14%	0.08%	0.420
DIS	DIS	0.083	0.01%	0.01%	0.429

Table 3. Building parameters and variables.

$T_a$	ambient air temperature (${}^{\circ }\mathrm{C}$)
$T_n$	air temperature of room n (${}^{\circ }\mathrm{C}$)
$T_{c,n}$	core temperature of room n (${}^{\circ }\mathrm{C}$)
$k_n$	thermal conductance between $T_n$ and $T_a$ ($\mathrm{W}/\mathrm{K}$)
$k_{r,n}$	thermal conductance between $T_{c,n}$ and $T_n$ ($\mathrm{W}/\mathrm{K}$)
$k_{n,j}$	thermal conductance between $T_n$ and $T_j$ ($\mathrm{W}/\mathrm{K}$)
$c_n$	thermal capacitance of room n ($\mathrm{J}/\mathrm{K}$)

Table 4. Performance of decentralised and distributed PFD and AFD architectures for Example 5.2.

PFD
Input	est.	$\hat{J}$	$P_{\mathrm{MD}}$	$P_{\mathrm{FA}}$	$T_{\mathrm{on}-\mathrm{line}}$ [s]
Switch	DEC	65.4	75.6%	0.0%	0.704
AFD
Design	est.	$\hat{J}$	$P_{\mathrm{MD}}$	$P_{\mathrm{FA}}$	$T_{\mathrm{on}-\mathrm{line}}$ [s]
DEC	DEC	35.8	26.5%	1.8%	0.775
	DIS	19.9	3.0%	2.1%	0.871
DIS	DIS	18.8	2.8%	1.9%	0.875