Available online at www.sciencedirect.com
ScienceDirect Procedia CIRP 60 (2017) 332 – 337
27th CIRP Design 2017
Product Family Flexible Design Method based on Dynamic Requirements Uncertainty Analysis Wei Weia,*, Jun Jib, Thorsten WuestcˈFei Taoa a
c
Advanced Manufacturing Technology and Systems Research Center, Beihang University, Beijing, China, 100191. b Information Center of China North Industries Group Corporation, Beijing 100089, China. Industrial and Management Systems Engineering Department, Benjamin M. Statler College of Engineering and Mineral Resources, West Virginia University, Morgantown, WV 26506, United States.
* Corresponding author. E-mail address:
[email protected]
Abstract Developing product families has been recognized as an efficient and effective means to realize sufficient product variety to satisfy a range of customer and support mass customization manufacturing. This paper presents a product family flexible design method based on dynamic requirements uncertainty analysis. The product family dynamic uncertain requirements analysis and forecasting techniques is researched in this paper, aims to improve the dynamic response ability of the product family to the change of the market demand in the future. Firstly, the multi-domain transmission mode of dynamic requirements was discussed and the product family flexible design model was proposed. Then the sensibility of design parameter to dynamic requirements was analyzed and the variation index of design parameter was calculated. As a result, the product platform of product family flexible design was constructed. A product family flexible design prototype system was also developed, and the application verification for flexible design of forging press product family was carried out to demonstrate the validity of the proposed method. © Published by Elsevier B.V. This 2017The TheAuthors. Authors. Published by Elsevier B.V.is an open access article under the CC BY-NC-ND license ©2017 (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 27th CIRP Design Conference 2017. Peer-review under responsibility of the scientific committee of the 27th CIRP Design Conference
Keywords: Product Family; Flexible Design; Dynamic Requirements; Uncertainty analysis; Immune clonal algorithm;
A.
INTRODUCTION
As the more effective method to meet the growing individual request, the technology of platform-based product development was the hot topic in the past few years, the product platform offer plenty of benefit: different products which come from the same platform can share a core set of common platform elements. As a result, company can reduce development time and costs, simplify system complexity and improve the ability of upgrade products. But the weakness of platform-based product development exposed gradually. Due to the product family members share too many common elements to highlight individuality. For that reason, the research on flexible product family design is worth. Compare with product platform, the flexible product platform consider the uncertainty factors includes the product development in the future. The flexible platform based on dynamic requirements uncertainty is the more effective method to meet problem of mass customization.
In the few years, scholars have done a lot of researches on the question of flexible platform and dynamic requirements uncertainty. Suh E S [1] proposed a flexible platform strategy by incorporating flexibility into product platforms, the design process generate multiple design alternatives by analysis demand uncertainty [2], and then filtered the profitable flexible component design with minimum cost and economic profitability, the proposed process was demonstrated in automotive application case. Q Ma [3] integrated the method of parametric design into flexible product platform, and presented a rapid design method base on flexible product platform by adjusting key parametric, the application on belt conveyor demonstrated this method fit the problem of product family design efficiently. Kangyun Shi [4] combined the advantages of the modular-based and the scale-base product platform design, analyzed the unknown uncertainties related to customer needs, find out the key design parameters, through mapping between
2212-8271 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 27th CIRP Design Conference doi:10.1016/j.procir.2017.01.037
333
Wei Wei et al. / Procedia CIRP 60 (2017) 332 – 337
the parameters and the physical structure, the critical flexible elements were determined, and the flexible product platform was constructed by extracting the common and the flexible elements. Uncertainty was a concept appeared in the field of philosophy, statistics, economics, psychology and engineering science. Aim at the optimization problem of uncertain structures design, J Cheng [5]~[6] proposed a constrained interval optimization model firstly, Mechanical performance indices was described as the objective and constraint functions of the design vector and interval uncertain parameters in this model. An algorithm integrating radial basis function, interval analysis, and non-dominated sorting genetic algorithm (NSGA-II) was put forward to solve the optimization problem of uncertain structures design. Paper [7] believed uncertainty was composed by inner-uncertainty and outer-uncertainty. A large number of researches about dynamic uncertain requirements forecasting method were done in Paper [8] ~ [11]. Concept of flexible product platform was introduced to improve the ability of product family dynamic response to market changes. After discussed the multi-domain transmission mode of dynamic requirements. A two-stage multi-objective optimization based platform design methodology (MOPDM) is proposed. Finally, universal motor platform is designed by the process proposed in this paper. The result shows that the method this paper proposed is better than one-stage MOPDM. B.
The Mathematic Model of Dynamic Requirements Uncertainty
requirements Product development process is described by four design-domains according to axiomatic design theory. There is different design variables in each domain, it can also be described custom needs, function requirements, design parameters and process variables. The neighboring domain can impact each by variable mapping. It can be seen from Fig.1, changes in customer’s requirements can be mapped to the change of the function and structure of product. The dynamic needs lead to various products. It is a complex problem to balance the ability of evolution and development time. In conclusion, market uncertainty cause the structure’s uncertainty. Design Task
CN1 CN2 ⁞ CNn
$
ª U U « « U U « « «UP UP « « ¬«UV UV
UN UN
UPN
UVN
(1)
UQ º » UQ » » » UPQ » » » UVQ ¼»
(2)
Where, ULM means the impact of the j -th function to i -th request. The bigger the ULM is, the more important M -th function is to the i -th request: 0 rij 1 .
2) Analysis and Forecast of dynamic requirements
Uncertainty Customer requirements always is fuzzy and uncertain, the fuzzy mathematical theory [12] is applied in this paper to convert the uncertain requirements into numerical model. The demands intensity can be divided into six levels, and defined by the values in Table 1: Table 1 Demand intensity and the corresponding value evaluation index Intensity strongest stronger common Value
9
7
weak
5
3
weaker Irrelevant 1
0
A matrix about the requirement important is established: (3) >9 9 9 1 9 1 @ 9 Where V means the demand intensity matrix, where V1ˈ V2,VN can only value from the table1.
1) the multi-domain transmission mode of dynamic
Consumer Domain (CNs)
)5 ½ ° ° ° ° $® ¾ ° ° °¯)5 Q °¿
&1 ½ ° ° ° ° ¾ ® ° ° °¯&1 V °¿
product design function domain (FRn) FR1 FR2 FR3 ⁞ FRn
physical domain (DPm)
product manufacture
DP1 ⁞ DPh DPl ⁞ DPm
process domain (PVp) ⁞ PVe ⁞ PVg ⁞ PVi ⁞
Due to requirements can be mapped to function, the delphi technique [13] is applied to complete the requirement – function matrix˖
%
ª « « , « ,, 9« « « 1 « ¬«680
$ % 0 [,$ [,% [,0 [,,$ [,,% [,,0
[1$ $N
The mapping-relationship between consumer domain and function domain can described by the formula (1), A is named as request-function matrix.
[1% %N
0N
[10
(4)
» » 16 » » ¼»
Where, [ 10 means degree the function 0 -th contributes to the requirement 1 -th, 1 6 means the importance of the 1 -th requirement among all the requirements, the higher 1 6 is, the more important this requirement is, 0 N means the contribution to all the requirements. The higher 0 N is, the more importance function is. The importance higher than liminal value I is regarded as important requirements, and contribution higher than liminal value M is regarded as key functions. As result: >&1 &1 &1 [ @ &1 (5) )5
Fig 1. The multi-domain transmission mode
680 º » ,V » ,, V »
>)5
)5 )5 = @
334
Wei Wei et al. / Procedia CIRP 60 (2017) 332 – 337
C.
Flexible Platform Design based on Dynamic Requirements Uncertainty Analysis
3) The sensitivity of design parameters on the analysis of demand uncertainty There is multiply design-parameters in product family, before establishing the product platform, the important thing is divided those design-parameters into the common platform parameters and the non-platform variables according to their properties. The result of division will affect the commonality of product platform. In order to divide those parameter objectively, the concept of sensitivity [14] and variation index [15] are introduced to assist the parameter divide-process. Sensitivity shows the influence degree of design parameter on the product performance, the small sensitivity parameters can be regarded as constant parameters in platform, which can be optimized on the platform, the large sensitivity parameters can be regarded as variable parameters, which can be optimized on the product. The variation index represent the variation degree of design parameter. For the platform, the bigger the sensitivity, the smaller the index, the better the platform. First partial derivative method is utilized to calculate the sensitivity of each parameter. Supposing the target function of product performance is ) [ ^I [ I [ I [ `( P is the number of performance), when [ 3 N ^[[ [ Q `( Q is the number of parameter) make ) [ get the best result, the product 3 N ’s sensitivity N of M -th to L -th performance in the is 3 -th product can be described as: 'IL [ (6) 0 LMN
'[ M
Where: '[ M means minor changes of parameter [ ; 'IL [ is fluctuation of L -th product performance cause
by the minor changes of parameter [ . N Formula (7) is the sensitivity matrix about the 3 -th product, which presents all the parameter’s fluctuation to all the product performance.
0N
ª 'I [ « '[ « « 'I [ « '[ « « ' I [ « «¬ '[ Q
'I [ '[ 'I [ '[ 'I [ '[ Q
M
The global sensitivity of
'I P [ º '[ »» 'I P [ » '[ » » » 'I P [ » '[ Q »¼
(7)
-th design parameter is:
+
0 *LM
0 LMN ¦ N
(8)
+
Where: 0 LMN is the local sensitivity about N -th product of M -th design parameter to L -th performance; + is the number of product which come from product family. The variation index of product can be measured by mean and variance: (9) GM G M PM Where, G M is variation index of the design parameter, P M is mean of [ M , G M is variance of [ M . After get the sensitivity and variation index, the liminal value O of sensitivity, liminal value O of variation index
should be gave subjectively, and The parameters whose sensitivity higher than O and variation index higher than E is regarded as design variable parameters, other parameters can be regarded as design constant parameters. 4) The process of two-stage multi-objective optimization based platform design methodology Many researches used one-stage optimization procedure which optimized the platform settings and corresponding members of family in one stage. When the number of design variables increase, the dimensionality of the optimization problems become too complex and expensive to be dealt only by one optimization algorithm. A two-stage optimization approaches is proposed, which divides the task into two stages: first, decide which variables are shared and their settings for platform configuration, second, generate all product’s optimal values for variables. As it shows in Fig 2.
Platform Design
Indicidual Design
Perform DOE
Combine CI and PI
Design Model 0LQ 0D[)˄[˅
EM OA
I [ IQ [
Fig. 2.
Calculate mean and standard deviation of design variables
EM OA
Best compromise solution
Optimization framework of MOPDM
In Fig2, the multi-objective optimization evolutionary algorithm (EMOA) is applied twice. CI denotes the similarity factor of design variables among instance products and PI expresses the general performances of product family. They are two competing objectives during the design of scale-based product platform. The particular optimization steps of the MOPDM are given next: Step1: Identify the design variables through product analysis. Step2: Perform DOE to check for possible reduction of design variables. Step3: Identify the constraints and multi-objectives for optimization Step4: Make sample runs to determine best MOEA parameters for the problem and optimize every instance independently base on MOEA Step5: Calculate mean (mi) and standard deviation (δi) of design variables, then identify platform common parameter and scaling variable sets by δi /mi Step6: Set platform common parameters as mi., identify the constraints and design variables. Step7: Optimization to derivative products based on platform common parameters using MOEA. D.
The Overview of Product Family Flexible Design Method Based on Dynamic Requirements Uncertainty Analysis
The process model of flexible platform based on dynamic requirements uncertainty is illustrated in Fig.3. Firstly, get the requirements form custom, through fuzzy mathematic theory
335
Wei Wei et al. / Procedia CIRP 60 (2017) 332 – 337
and delphi technique, converting the uncertain requirements to important requirements CN and key function FR. Second, divide design parameters into common parameters P and the scaling variables V based on the sensitivity and variation index. Third, after the design parameter is reduced, according to the design function and constraints of product family, while keeping the common parameters constant, the scaling Uncertain requirement acquisition and determination Requiremens get 9 >9 9 91 91 @ Customer Uncertain Requirements % &1
ª&1 º « » «&1» « » « » ¬&1Q ¼
ª « «, « ,, 9« « «1 « ¬«680
&1
$ % 0 680º » [,$ [,% [,0 ,V » [,,$ [,,% [,,0 ,,V »
[1$ [1% [10 $N %N 0 N
» » 16 » » ¼»
Important requirement and key function select
ª&1 º « » «&1 » « » « » ¬&1V ¼
variables are scaled up or down to form a series of derivative products and optimization every derivative products. For a single derivative product i, platform common parameters and scaling variables constitute all design variables. Furthermore, the product family is composed of the scale-based product platform and its derivative instances.
The first-stage(determine common parameters)
Second stage(optimization every case)
Common Parameters GM GM PM
Constant Design Parameter
Key function and important requirements
3L 3L L ˈ ˈ ˈP
MOPDM
0N ª)5 º « » )5 )5 « » « » « » ¬)5N ¼
Product 1 3 9
Product 2 3 9
MOPDM Product i
ª'I [ 'I [ 'I [ º P » « '[ '[ '[ » « «'I [ 'I [ 'IP [ » « '[ '[ '[ » « » » « «'I [ 'I [ 'IP [ » «¬ '[Q '[Q '[Q »¼
Scaled Design Parameter 9M 9M M
3 9L
Product k
ˈ ˈ ˈQ
3 9N
Scaled Parameters
Fig 3. The development process of flexible product family
E.
CASE ILLUSTRATION: SERIES OF TRACTION MACHINE PLATFORMS
5) The uncertain requirement acquired and analyzed Motor is a kind of very common power plant, the example of one motor manufacturing company’s portable motor product platform is taken to show the whole process of design product platform and product family, including how to transform uncertain demands to the certain demands, and then mapped demands to the design of design parameters. Finally, the proposed method is proved available. According to market survey, we get some requirements about the motor, CN= {easy to carry, save electricity, high precision}, motor function FR= {little-weight, high-efficiency, lower-price, large-torque}. Through the analysis and evaluation of experts, we get the requirement-function matrix bellow:
%
ª « « &1 « &1 « « &1 «¬680
)5
)5
)5
)5
680 º
» » » » » »¼
(10)
From the matrix, FR1 ǃ FR2 is the primary function, corresponding: little-weight and high-efficiency. CN1ǃCN2 is the main requirements, corresponding: easy to carry and save electricity. Therefore, weight and efficiency is the main design target about this platform. The optimization model of motor platforms is illustrated as: F = (max (torque), min (weight)). 6) Mathematical model of motor Motor platform can generate derivative motor just change the scale of the number of stack, keep the constants design variable same. The motor platform is a typical scale-based product platform. Design a family of same power motors that satisfies a variety of torque by scaling a common motor platform around some scaling variables of the motor [16].
0 ° °K ° ° °0 ° °0 ° ° °0 ® °3 ° ORVV ° ° °5 D ° ° ° °5 V ° ¯
0 0 0
(11)
3LQ 3ORVV 3LQ
3RXW 3LQ
>
@
S 5 5 K K UV S 5 ^>K
K
K K UV
5 K K @= F 6 ZD >K 5 K @= V 6 ZI `UF
, 5 D 5 V , U >K 5 K K @= F 6 ZLUH U >K 5 K @= V
6 ZLUH
The torque of motor: 7
1F ), S
(12)
The range of design variable and the constraint conditions of each design variable are shown in Table 2, the bold font section is the design parameters. In order to convert two optimizing problem to the minimum problem, the maximal efficiency (η=Pout/Pin) is transferred into the minimal efficiency loss (ηloss=1-η=Ploss/Pin). Table 2 Main design parameters information
Parameter Name M M1 M2
Parameter Meaning weight of motor weight of stator weight of motor armature
Value Ranges/ Constraint Condition M İ 2.5Kg -
M3
weight of motor coil
-
¨
efficiency of motor
¨≥ 25%
Pout
output power
P = 300
336
Wei Wei et al. / Procedia CIRP 60 (2017) 332 – 337
Pin
input power
Ploss
loss power
T
torque of motor
Rs
resistance of wire
Ra
resistance of armature
T={0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5}N·m R > h1
R
outer diameter of stator
h1
thickness of stator
1 ≤ h1 ≤ 15mm
h2
stack thickness of stator
1 ≤h2 ≤ 7mm
²s
density of steel
7800Kg/m3
h3
gap of air
0.5mm
1 ≤ R ≤ 10mm
Zc
number of rotor turns
100 ≤ Zc ≤ 1500
Swa
cross-section of rotor coil
0.2 ≤ Swa ≤ 2.0 m2
Zs
number of stator turns
100 ≤ Zs ≤ 600
Swf
cross-section of stator coil
0.2 ≤ Swf ≤ 2.0m2
²c
density of wire
8900 Kg/m3
Swire
cross-section of wire
19.625h10-6m3
ρ
electrical resistivity of wire
0.0172μ¡gm
I
Current size
0 ≤ I ≤ 5A
7) Motor platform of product family design optimization The multi-objective optimization model about the motor platform is established; in this stage, artificial immune algorithm is used to calculate the sensitivity and the variation index of design variables. Take the different torque requirement as constraint condition, take the design parameter as the optimization object, take the weight and the efficiency as the optimization objective. Set the scale of antibodys group Pop=500, maximum times of iterations G=1000, the probability of crossover immune operation p=0.6. The result is shown in fig4 (a)-(h). With the increase of torque, the efficiency loss and weight also increase, but the overall trend is identical. Choose the comprehensive optimal result (the pareto result which get the best result as the formula P )) from those results. U PK P0 ( P
(c)T=0.15N·m
(e)T=0.25N·m
(g)T=0.25N·m
(d) T=0.2N·m
(f) T=0.3N·m
(h) T=0.3N·m
Fig. 4. The process of improved immune clonal algorithm
In the first stage, the comprehensive optimal result is regarded as the best result, the sensitivity and of every design parameter to the optimization target from the comprehensive optimal result. When solving the sensitivity of design parameters to design targets, the design parameters take different values, save those values and calculate the average, variance and variation index through the equation (9). the threshold of sensitivity is set¬1= 0.20 for weight target, the threshold of sensitivity is set¬2= 0.15 for efficiency target; the threshold of variation index is set£= 10%. The design variables {Swf, Swa, R, I} are the common platform parameters; {h2, Zc, Zs, h1} are the non-platform variables average as the value common platform parameter, {I = 4.1, Swf = 0. 35, t
(a)T=0.05N·m
(b) T=0.1N·m
=5.6, Swa = 0.22}. 8) Examples of motor design optimization After ensure the common parameter, just adjust the design parameter to make the weight and efficiency get the best both, so, single product instance will optimized by improved artificial immune algorithm. the value table 3 is the finally result after optimization and selection.
Wei Wei et al. / Procedia CIRP 60 (2017) 332 – 337 Table 3 Optimization result of electromotor design product instance common platform parameters
ID
non-platform variables
G.
Optimization Results
h2
Zc
Zs
h1
Swa
R
Swf
I
M
¨
1
0.87
685
47
5.6
0.22
2.3
0.22
3.12
0.44
73.18
2
1.15
710
71
5.6
0.22
2.3
0.22
3.37
0.48
71.93
3
1.52
748
62
5.6
0.22
2.3
0.22
3.56
0.53
70.07
4
1.95
816
67
5.6
0.22
2.3
0.22
3.91
0.62
68.69
5
2.31
882
85
5.6
0.22
2.3
0.22
4.29
0.69
64.84
6
2.67
965
75
5.6
0.22
2.3
0.22
4.52
0.75
60.33
7
3.02
1068
79
5.6
0.22
2.3
0.22
4.85
0.87
57.46
8
3.45
1120
65
5.6
0.22
2.3
0.22
5.15
0.96
53.62
9) Comparison of results between different optimization algorithms Table 4 Comparison of results obtained by different optimization algorithms Optimization algorithm
Diversity
Convergence
Run time(s)
One-stage MOPDM
0.281 7
0.3067
47.8
Two-stage MOPDM
0.2653
0.3562
27.5
PPCEM
0.3192
0.3289
37.9
In table 4, the product platform concept exploration method (PPCEM) was proposed in 2001 by Simpson. This method is the very classic method in the field of product family design. In order to compare the efficiency and performance of PPCEM and the method this paper proposed, the concept of Frontier Approaching Criteria [17] and Set of Decentralized Diversity Criteria [18] are introduced. As to the Frontier Approaching Criteria, bigger approaching the leading edge value is, better the convergence is. As to the Set of Decentralized Diversity Criteria, smaller the solution sets disperse the various values is, better the diversity of pareto is. The result in table4 is average value after ten times calculate in one computer. The result shows that the method this paper proposed is better in the pareto diversity, pareto convergence and efficiency. F.
Conclusion and Future Work
In allusion to product family flexible design, first, this paper discusses the multi-domain transmission mode of dynamic requirements, researches the requirements analysis and forecasting techniques, and proposes a two-stage product family flexible design method, introduce the sensitivity and variation index to filtrate the common platform parameters in the first stage. Then, this paper proposes an improved artificial immune algorithm, because the fitness function is evolutionary change, that made more accurate in filtrating common platform parameters; this algorithm has stronger global searching ability and local search ability, and the stress in global search at the same time takes into account the local search. At last, the developed method is better than one-stage multi-objective optimization based platform design methodology.
Acknowledgment
This research is supported by the National Natural Science Foundation of China (Grant number 51675028, 51505437) and the Fundamental Research Funds for the Central Universities. H.
Reference
[1] Suh E S, Weck O L D, Chang D. Flexible product platforms: framework and case study[J]. Research in Engineering Design, 2007, 18(2):67-89. [2] Suh E S, Weck O L D, Chang D. Flexible product platforms: framework and case study. Research in Engineering Design, 2007, 18(2):67-89. [3] Ma Q, Tan R, Jiang P, et al. Flexible Product Platform Based on Design Parameters. Building Innovation Pipelines through Computer-Aided Innovation, 2011:7-15. [4] Kang Yunshi, Based on the flexible product platform of product family development. Computer Integrated Manufacturing System, 2009, 15(10):1880-1889. [5] Cheng J, Liu Z, Wu Z, et al. Direct optimization of uncertain structures based on degree of interval constraint violation[J]. Computers & Structures, 2016, 164:83-94. [6] Cheng J, Duan G F, Liu Z Y. Interval multiobjective optimization of structures based on radial basis function, interval analysis, and NSGA-II[J]. Journal of Zhejiang University-SCIENCE A, 2014, 15(10):774-788. [7] Miller R, Lessard D R. Evolving Strategy: Risk Management and the Shaping of Large Engineering Projects. Ssm Electronic Journal, 2007. [8] Halpern J Y. Reasoning about uncertainty. MIT press, 2005. [9] De Weck O L, Neufville R D, Chaize M. Staged deployment of communications satellite constellations in low earth orbit. Journal of Aerospace Computing, Information, and Communication, 2004, 1(3): 119-136. [10] De Neufville R, de Weck O, Frey D, et al. Uncertainty management for engineering systems planning and design. Engineering Systems Symposium, MIT, Cambridge, MA. 2004. [11] Silver M, Deweck O. Time-expanded decision network methodology for designing evaluable systems. Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Portsmouth, USA: AIAA, 2006:6-8. [12] Peter Guttorp. Fuzzy Mathematical Models in Engineering and Management Science[M]. Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co, 1990. [13] Linstone H A, Turoff M. The Delphi method: Techniques and applications[J]. Journal of Marketing Research, 1975, 18(3):363-364. [14] Scott M J, Antonsson E K. Using indifference points in engineering decisions. Imprecision in Engineering Design, 2000: 225. [15] Chen Y L, Chu W L, Xu Y S. Adaptability-oriented parametric product platform design. Computer Integrated Manufacturing Systems, 2007, 13(5): 877-884. [16] Simpson T W, Maier J R, Mistree F. Product platform design: Method and application. Research in Engineering Design, 2001.13(1): 2-22. [17] Zitzler E, Deb K, Thiele LˊComparison of multi-objective evolutionary algorithms: Empirical results. IEEE Transactions on Evolutionary Computation, 2000, 18(2) : 173-195ˊ [18] Deb K, Pratap A, Agarwal S. A fast and elitist multi-objective genetic algorithm: NSGA-IIˊIEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197ˊ
337
