Multi-solution pipe-routing method for the aeroengine with route constraints based on multi-objective optimization

Abstract

The complexity of aeroengine external piping systems necessitates the implementation of automated design processes to reduce the duration of the design cycle. However, existing routing algorithms often fail to meet designer requirements because of the limitations in providing a single solution and the inadequate consideration for route constraints. In this study, we propose the multi-solution pipe-routing method for aeroengines. This method utilizes a hybrid encoding approach by incorporating fixed-length encoding to represent route constraints and variable-length encoding and indicate free-exploration points. This approach enables designers to specify route constraints and iterate over the appropriate number of control points by employing a modified genetic iteration mechanism for variable-length encoding. Furthermore, we employ a pipe-shaped clustering niche method to enhance result diversity. The practicability of the newly proposed method is confirmed through comparative experiments and simulations based on the “AeroPiping” system developed on Siemens NX. Typical solutions demonstrate significant differences in circumferential and axial orientations while still satisfying engineering constraints.

Graphical abstract

Keywords

aeroengine / multi-solution pipe-routing / niche method / hybrid swarm optimization / multi-objective optimization / particle swarm optimization

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Nomenclature

Abbreviations
AABB	Axis-aligned bounding box
ACO	Ant colony algorithm
DE	Differential evolution
GA	Genetic algorithm
MOPSO	Multi-objective particle swarm optimization
MSPR	Multi-solution pipe-routing
OBB	Oriented bounding box
PSO	Particle swarm optimization
Variables
C	Pipe shape cluster
CD	Differential scaling factor
Cp	Crossover probability
c	Probability of the corresponding operation occurring
D	Dimension of problem
Dm	Distance between the two endpoints of the planned pipe segment
d_{\text{c}}^1	Extension distance in the normal direction at the clamp
d_{\text{c}}^2	Backward extension distance in the normal direction at the clamp
d_{\text{p}}^1	Extension distance in the normal direction at the parallel pipe
d_{\text{p}}^2	Backward extension distance in the normal direction at the parallel pipe
d_{\text{w}}^1	Extension distance in the direction Vw at the waypoint
d_{\text{w}}^2	Backward extension distance in the direction Vw at the waypoint
E	Square error
F(x)	Function for objective
f1	Function for evaluating pipe length
f2	Function for evaluating the degree to which the pipe is arranged along the circumference and axis
f3	Function for describe the distance between pipes and engine casing
f4	Function for evaluating the number of control points
hbounds	Function for evaluating out-of-bounds penalty
hlength	Function for evaluating length requirement penalty
hobs	Function for evaluating interference penalty
hpos	Function for evaluating improper point position penalty
I	Interference result
k	Number of clusters
l_{\text{ac}}^i	Length of the ith pipe segment arranged along the axial and circumferential directions
lE	Extension distance in the normal direction at the end port
li	Length of the ith pipe segment
lmin	Minimum length of pipe segments required by the process
lS	Extension distance in the normal direction at the start port
lsuit	Suitable length for pipe segment
lsuitmin, lsuitmax	Minimum and maximum suitable length for pipe segment
M	grid matrix
m	Number of populations
[Nr,Nθ,Nz]	Resolution of the matrix
\left\{n_{\text{r}}^i,n_{\text{θ}}^i,n_{\text{z}}^i\right\}	Matrix index value corresponding to point {ri,θi,zi}
N1,N2,N3,N4	Operations of mutation, crossover, addition, and reduction point operations
n	Number of pipe segments
nbounds	Number of discrete points in the pipe segment out of bounds
nc	Number of clamp constraints
nobs	Number of interfere discrete points
np	Number of parallel pipe constraints
npos	Number of wrong control points
nvl	Number of control points for initializing variable-length segments
nw	Number of waypoints constraints
Oi	Feasible solution obtained
Pbc	Preset bending count
pc	Random number used to determine whether to leave
pf	Free control point
{ρf,θf,zf}	Cylindrical coordinates of the point pf
Rc(z)	Function for the generatrix of the casing
Sps	Pipe shape set
T	Total number of iterations
t	Current iteration number
Vi,t	Current velocity of the ith individual in generation t
Vi,t+1	Updated velocity of the ith individual in generation t
Xe,t	Fixed-length encoding of the corresponding elite individual
Xi,t	Fixed-length encoding of the ith individual in generation t
Xi,t+1	Fixed-length encoding after flight
Xp,t	Individual optimal fixed-length encoding of the ith individual
Yi,t	Variable-length encoding of the ith individual in generation t
Zmin	Minimum boundary value in the axial direction
ω1	Scaling factor for f1
ω2	Scaling factor for lmin
ω3	Scaling factor for f3
ω4	Inertia factor
ω5	Self-learning factor
ω6	Best learning factor
μi	Mean vector of cluster Ci
γi	Angle for ith pipe segment projection with the x-axis
θmin	Circumferential minimum boundary value
ρc	Minimum radius of the engine casing
ρi	Radius of the ith pipe control point

Acknowledgements

This work was supported by the National Science and Technology Major Project, China (Grant No. J2019-I-0008-0008).

Conflict of Interest

The authors declare no conflict of interest.

RIGHTS & PERMISSIONS

2024 Higher Education Press