Multi-objective optimization of electro-pneumatic braking process with fuzzy logic control for heavy haul railway applications

Figures & data

Figure 1. Kinetic diagram.

Table 1. Locomotives and freight cars parameter.

Longitudinal train dynamics parameters
	Locomotives		Freight cars
Parameters	${\dot{x}}_{\mathit{n}}\le 0.1$	${\dot{x}}_{\mathit{n}}>0.1$	${\dot{x}}_{\mathit{n}}\le 0.1$	${\dot{x}}_{\mathit{n}}>0.1$
$A_1$	5	0.1	15	0.15
$A_2$	425	8.5	425	4.25
$\mathit{B}$	0	0.00938	0	0.007
$\mathit{C}$	0	0.0046	0	0.000325
Mass $m_n$	$162\times {10}^3$ kg		$106.5\times {10}^3$ kg
Number of axis $N_a$	5		4

Figure 2. Locomotive traction and dynamic brake curves.

Figure 3. Friction draft gear model: (a) loading stage 1, (b) loading stage 2, (c) unloading stage 1 and (d) unloading stage 2; 1- follower, 2- central wedge, 3- wedge shoe, 4- release spring, 5- outer stationary plate, 6- movable plate 7- lubricating metal, 8- inner stationary plate, 9- spring seat, 10- main springs, and 11- housing.

Figure 4. Brake model schematic.

Figure 5. Train traction and braking schedule according to the railroad position.

Figure 6. Fuzzy logic optimizable membership functions.

Table 2. Fuzzy control rules.

Speed	Acceleration input
input	$L_{\mathit{A}1}$	$L_{\mathit{A}2}$	$L_{\mathit{A}3}$	$L_{\mathit{A}4}$	$L_{\mathit{A}5}$
$L_{\mathit{S}1}$	$R_{\mathit{P}1}$	$R_{\mathit{P}2}$	$R_{\mathit{P}3}$	$R_{\mathit{P}4}$	$R_{\mathit{P}5}$
	$R_{\mathit{D}1}$	$R_{\mathit{D}2}$	$R_{\mathit{D}3}$	$R_{\mathit{D}4}$	$R_{\mathit{D}5}$
	$W_{\mathit{PD}1}$	$W_{\mathit{PD}2}$	$W_{\mathit{PD}3}$	$W_{\mathit{PD}4}$	$W_{\mathit{PD}5}$
$L_{\mathit{S}2}$	$R_{\mathit{P}6}$	$R_{\mathit{P}7}$	$R_{\mathit{P}8}$	$R_{\mathit{P}9}$	$R_{\mathit{P}10}$
	$R_{\mathit{D}6}$	$R_{\mathit{D}7}$	$R_{\mathit{D}8}$	$R_{\mathit{D}9}$	$R_{\mathit{D}10}$
	$W_{\mathit{PD}6}$	$W_{\mathit{PD}7}$	$W_{\mathit{PD}8}$	$W_{\mathit{PD}9}$	$W_{\mathit{PD}10}$
$L_{\mathit{S}3}$	$R_{\mathit{P}11}$	$R_{\mathit{P}12}$	$R_{\mathit{P}13}$	$R_{\mathit{P}14}$	$R_{\mathit{P}15}$
	$R_{\mathit{D}11}$	$R_{\mathit{D}12}$	$R_{\mathit{D}13}$	$R_{\mathit{D}14}$	$R_{\mathit{D}15}$
	$W_{\mathit{PD}11}$	$W_{\mathit{PD}12}$	$W_{\mathit{PD}13}$	$W_{\mathit{PD}14}$	$W_{\mathit{PD}15}$
$L_{\mathit{S}4}$	$R_{\mathit{P}16}$	$R_{\mathit{P}17}$	$R_{\mathit{P}18}$	$R_{\mathit{P}19}$	$R_{\mathit{P}20}$
	$R_{\mathit{D}16}$	$R_{\mathit{D}17}$	$R_{\mathit{D}18}$	$R_{\mathit{D}19}$	$R_{\mathit{D}20}$
	$W_{\mathit{PD}16}$	$W_{\mathit{PD}17}$	$W_{\mathit{PD}18}$	$W_{\mathit{PD}19}$	$W_{\mathit{PD}20}$
$L_{\mathit{S}5}$	$R_{\mathit{P}21}$	$R_{\mathit{P}22}$	$R_{\mathit{P}23}$	$R_{\mathit{P}24}$	$R_{\mathit{P}25}$
	$R_{\mathit{D}21}$	$R_{\mathit{D}22}$	$R_{\mathit{D}23}$	$R_{\mathit{D}24}$	$R_{\mathit{D}25}$
	$W_{\mathit{PD}21}$	$W_{\mathit{PD}22}$	$W_{\mathit{PD}23}$	$W_{\mathit{PD}24}$	$W_{\mathit{PD}25}$

Figure 7. Optimized solutions.

Table 3. Standard and optimized results.

	Results
	Dissipated	Draft gear peak force		Expended	Average
	energy	Traction	Buff	time	speed
Configurations	[MJ]	[kN]	[kN]	[s]	[km/h]
Standard ABDX	7835	1090	−1139	614.6	50.15
Equivalent	7956	1090	−1139	625.7	49.65
Electro-pneumatic
Min. $f_1(\mathbf{X})$	6246	1031	−1130	544.4	53.58
Min. $f_2(\mathbf{X})$	7301	840	−1122	615.8	50.10
Min. $f_3(\mathbf{X})$	7705	1060	−1073	627.6	49.57
Max. $\mathit{Ft}(\mathbf{X})$	6784	935	−1103	613.9	50.18

Figure 8. Draft gear peak forces – standard schedule.

Figure 9. Rolling-stock speed and braking cylinder pressure in the downhill section.

Figure 10. Draft gear peak forces – best of each criterion.

Figure 11. Draft gear peak forces for the best trade-off solution.