A novel approach for remanufacturing process planning considering uncertain and fuzzy information

doi:10.1007/s11465-021-0639-1

Front. Mech. Eng.

2021, Vol. 16

Issue (3) : 546-558 https://doi.org/10.1007/s11465-021-0639-1

RESEARCH ARTICLE

A novel approach for remanufacturing process planning considering uncertain and fuzzy information

Yan LV¹, Congbo LI¹(

), Xikun ZHAO¹, Lingling LI², Juan LI¹

¹. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China
². College of Engineering and Technology, Southwest University, Chongqing 400715, China

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Abstract

Remanufacturing, as one of the optimal disposals of end-of-life products, can bring tremendous economic and ecological benefits. Remanufacturing process planning is facing an immense challenge due to uncertainties and fuzziness of recoverable products in damage conditions and remanufacturing quality requirements. Although researchers have studied the influence of uncertainties on remanufacturing process planning, very few of them comprehensively studied the interactions among damage conditions and quality requirements that involve uncertain, fuzzy information. Hence, this challenge in the context of uncertain, fuzzy information is undertaken in this paper, and a method for remanufacturing process planning is presented to maximize remanufacturing efficiency and minimize cost. In particular, the characteristics of uncertainties and fuzziness involved in the remanufacturing processes are explicitly analyzed. An optimization model is then developed to minimize remanufacturing time and cost. The solution is provided through an improved Takagi–Sugeno fuzzy neural network (T-S FNN) method. The effectiveness of the proposed approach is exemplified and elucidated by a case study. Results show that the training speed and accuracy of the improved T-S FNN method are 23.5% and 82.5% higher on average than those of the original method, respectively.

Keywords remanufacturing uncertain and fuzzy information process planning T-S FNN

Corresponding Author(s): Congbo LI

Just Accepted Date: 26 July 2021 Online First Date: 31 August 2021 Issue Date: 24 September 2021

Cite this article:

Yan LV,Congbo LI,Xikun ZHAO, et al. A novel approach for remanufacturing process planning considering uncertain and fuzzy information[J]. Front. Mech. Eng., 2021, 16(3): 546-558.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-021-0639-1
https://academic.hep.com.cn/fme/EN/Y2021/V16/I3/546

Fig.1 Framework of remanufacturing process planning.

Damage form	Damage amount interval	Damage degree	Quantified score interval	Calculation formula of score ( Q)
Abrasion	0	None	0	?
	0 < χ (wear amount) ≤ 0.6 mm	Slight	(0, 5)	$Q = 5 ? 0.6 ? χ 0.6 ? 0 × 5$
	0.6 mm < χ < 2.0 mm	Medium	[5, 10)	$Q = 10 ? 2 ? χ 2 ? 0.6 × 5$
	χ ≥ 2.0 mm	Severe	10	?
Corrosion	0	None	0	?
	0< δ (depth) ≤0.1 ?	Slight	(0, 5)	$Q = 5 ? 0.1 ? ? δ 0.1 ? ? 0 × 5$
	0.1 ? < δ < 0.2 ?	Medium	[5, 10)	$Q = 10 ? 0.2 ? ? δ 0.2 ? ? 0.1 ? × 5$
	δ ≥ 0.2 ?	Severe	10	?
Crack	0	None	0	?
	0 < θ (length) < 0.1 ?	General	(0, 10)	$Q = 10 ? 0.1 ? ? θ 0.1 ? ? 0 × 10$
	θ ≥ 0.1 ?	Severe	10	?
Deformation	0	None	0	?
	0 < ? (bending amount) ≤ 0.01 L	Slight	(0, 5)	$Q = 5 ? 0.01 L ? ? 0.01 L ? 0 × 5$
	0.01 L< ? < 0.02 L	Medium	[5, 10)	$Q = 10 ? 0.02 L ? ? 0.02 L ? 0.01 L × 5$
	? ≥ 0.02 L	Severe	10	?

Tab.1 Evaluation standard of damage score for a used machine tool spindle

Tab.2 Quality requirements of remanufacturing process planning for a used machine tool spindle

Fig.2 Remanufacturing process planning method for used components based on the improved T-S FNN.

Fig.3 T-S FNN prediction model for used components.

Fig.4 Convergence curve of T-S FNN training curve of (a) remanufacturing time and (b) remanufacturing cost.

Fig.5 Comparison of T-S FNN prediction and observed values. Comparison of (a) remanufacturing time and (b) remanufacturing cost obtained by the original model; comparison of (c) remanufacturing time and (d) remanufacturing cost obtained by the improved model.

Fig.6 Comparison of prediction errors of the two models.

Tab.3 Optional remanufacturing process plan for the spindle of used machine tools

Tab.4 Input and output of the T-S FNN prediction model

CNC	Computer numerical control
FCM	Fuzzy c-means
FNN	Fuzzy neural network
T-S FNN	Takagi–Sugeno fuzzy neural network
A _?0 and B _?0	Constant coefficients
A _?j and B _?j	Coefficients of x _?ij
c	Number of clusters of the simple
c ^N	Total number of nodes in the layer
D _i	Density index of the sample X _i
f ₁(?)	Remanufacturing time function
f ₂(?)	Remanufacturing cost function
h	Weight index
J(?) and J ^{( t)}	Objective function of FCM
k	Number of clusters
L	Length of the machine tool spindle (mm)
M _μ	Total number of components of type μ
N _c	Number of the fuzzification layer nodes
N _μ	Total number of attributes of components of type μ
P and P _w	Remanufacturing process plan
P _η	ηth optional remanufacturing process plan
$P η ?$	Optimal remanufacturing process plan
p _ηd	dth quality requirement parameter value of the optional remanufacturing process plan
Q and Q _l	Damage score
R and R _d	Standard value of quality requirement parameters
R ^{N× M}	N× M-dimensional real number space
r _a and r _b	Field radius
U and U ^{( t)}	Membership matrix
u _ki	Fuzzy membership degree
V and V ^{( t)}	Clustering center matrix
V _k ^*	Best clustering center matrix
V ⁽⁰⁾	Initial clustering center vector
$V ~ k ?$	Clustering center closest to $V k ?$
v _ki	Clustering center
$v k N ?$	Best clustering center
X	Used component sample
$X k ?$	Location of the initial clustering center of the kth sample
X _i	ith used component
X _?i	ith used component with type ?

x _ij	Attribute value of X _i (including damage score and parameter value of quality requirement)
x _?ij	jth attribute value of X _?i
y _s	Estimates of the remanufacturing time and cost
$y s k o$	Output value of the second layer of consequent network
y _η1	Remanufacturing time of the ηth process plan (h)
y _η2	Remanufacturing cost of the ηth process plan (CNY)
Z ^*	Minimum comprehensive objective value
Z _η	Comprehensive objective value of the remanufacturing time and cost
$α k o$	Applicability of each rule to x _ij
$α ˉ k o$	Normalized value of the applicability of each rule
β	Network learning rate
γ	Overlap coefficient
δ	Corrosion depth (mm)
ε	Permissible tolerance
η	Optional remanufacturing process plan number
θ	Crack length (mm)
μ ^k	Fuzzy membership degree matrix
$μ N k$	Fuzzy membership degree
$ρ k o j s$	Connection weight
σ _k	Width of the Gaussian function
φ _k	Gaussian function center matrix
φ _kN	Gaussian function center
?	Diameter of the machine tool spindle (mm)
$Ω$	Domain matrix
ω ₁	Weight value of remanufacturing time
ω ₂	Weight value of remanufacturing cost
?	Component type number
χ	Wear amount (mm)
?	Bending amount

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