Abstract

In this paper, we extend our previous work on a goal-oriented inverse design method to carry out inverse robust design by managing the uncertainty involved. The extension embodies the introduction of specific robust design goals and new robust solution constraints anchored in the mathematical constructs of Error Margin Indices (EMIs) and Design Capability Indices (DCIs) to determine “satisficing” robust design specifications across analytical model-based process chains. Contributions in this paper include the designer’s ability to explore satisficing robust solution regions when multiple conflicting goals and multiple sources of uncertainty are present. Using the goal-oriented inverse design method, robust solutions are propagated in an inverse manner. We demonstrate the efficacy of the method and the associated robust design functionalities using an industry-inspired hot rolling and cooling process chain example problem for the production of a steel rod. In this example, we showcase the formulation of multiple mechanical property goals for the end product using the robustness metrics and the exploration of satisficing robust solutions for material microstructure after the cooling process using the robust solution constraints. The robust solutions thus identified are communicated in an inverse manner using the design method to explore satisficing robust solutions for the microstructure generated after the hot rolling process. Using the example, we demonstrate the robust co-design of material, product, and associated manufacturing processes. The method and the associated design constructs are generic and support the formulation and inverse robust design exploration under uncertainty of similar problems involving a sequential, analytical model-based flow of information across process chains.

References

References
1.
Ashby
,
M. F.
, and
Cebon
,
D.
,
1993
, “
Materials Selection in Mechanical Design
,”
Le Journal de Physique IV
,
3
(
C7
), pp.
C7-1
C7-9
. 10.1051/jp4:1993701
2.
Norton
,
R. L.
,
1996
,
Machine Design: An Integrated Approach
,
Prentice-Hall Inc.
,
NJ
.
3.
Shigley
,
J. E.
,
1972
,
Mechanical Engineering Design
,
McGraw-Hill
,
New York
.
4.
Pahl
,
G.
, and
Beitz
,
W.
,
2013
,
Engineering Design: A Systematic Approach
,
Springer Science & Business Media
,
London
.
5.
Olson
,
G. B.
,
1997
, “
Computational Design of Hierarchically Structured Materials
,”
Science
,
277
(
5330
), pp.
1237
1242
. 10.1126/science.277.5330.1237
6.
McDowell
,
D. L.
,
Panchal
,
J.
,
Choi
,
H.-J.
,
Seepersad
,
C.
,
Allen
,
J.
, and
Mistree
,
F.
,
2009
,
Integrated Design of Multiscale, Multifunctional Materials and Products
,
Butterworth-Heinemann
,
Waltham, MA
.
7.
Horstemeyer
,
M. F.
,
2018
,
Integrated Computational Materials Engineering (ICME) for Metals: Concepts and Case Studies
,
John Wiley & Sons
,
Hoboken, NJ
.
8.
McDowell
,
D. L.
,
2018
, “
Microstructure-Sensitive Computational Structure-Property Relations in Materials Design
,”
Computational Materials System Design
,
D.
Shin
and
J.
Saal
, eds.,
Springer
,
Cham
, pp.
1
25
.
9.
Horstemeyer
,
M. F.
,
2012
,
Integrated Computational Materials Engineering (ICME) for Metals: Using Multiscale Modeling to Invigorate Engineering Design With Science
,
John Wiley & Sons
,
Hoboken, NJ
10.
Shahan
,
D. W.
, and
Seepersad
,
C. C.
,
2012
, “
Bayesian Network Classifiers for Set-Based Collaborative Design
,”
ASME J. Mech. Des.
,
134
(
7
), p.
071001
. 10.1115/1.4006323
11.
Matthews
,
J.
,
Klatt
,
T.
,
Morris
,
C.
,
Seepersad
,
C. C.
,
Haberman
,
M.
, and
Shahan
,
D.
,
2016
, “
Hierarchical Design of Negative Stiffness Metamaterials Using a Bayesian Network Classifier
,”
ASME J. Mech. Des.
,
138
(
4
), p.
041404
. 10.1115/1.4032774
12.
Li
,
C.
, and
Mahadevan
,
S.
,
2016
, “
Role of Calibration, Validation, and Relevance in Multi-Level Uncertainty Integration
,”
Reliab. Eng. Syst. Saf.
,
148
, pp.
32
43
. 10.1016/j.ress.2015.11.013
13.
Mullins
,
J.
, and
Mahadevan
,
S.
,
2016
, “
Bayesian Uncertainty Integration for Model Calibration, Validation, and Prediction
,”
J. Verification, Validation and Uncertainty Quantification
,
1
(
1
), p.
011006
. 10.1115/1.4032371
14.
Kalidindi
,
S. R.
,
2015
,
Hierarchical Materials Informatics: Novel Analytics for Materials Data
,
Elsevier
,
Waltham, MA
.
15.
McDowell
,
D. L.
, and
Kalidindi
,
S. R.
,
2016
, “
The Materials Innovation Ecosystem: A Key Enabler for the Materials Genome Initiative
,”
MRS Bulletin
,
41
(
4
), pp.
326
337
. 10.1557/mrs.2016.61
16.
McDowell
,
D. L.
, and
LeSar
,
R. A.
,
2016
, “
The Need for Microstructure Informatics in Process–Structure–Property Relations
,”
MRS Bulletin
,
41
(
8
), pp.
587
593
. 10.1557/mrs.2016.163
17.
Panchal
,
J. H.
,
Kalidindi
,
S. R.
, and
McDowell
,
D. L.
,
2013
, “
Key Computational Modeling Issues in Integrated Computational Materials Engineering
,”
Comput. Aided Des.
,
45
(
1
), pp.
4
25
. 10.1016/j.cad.2012.06.006
18.
McDowell
,
D. L.
, and
Olson
,
G.
,
2008
, “
Concurrent Design of Hierarchical Materials and Structures
,”
Sci. Model. Simul.
,”
15(
1
3),
pp.
207
240
. 10.1007/s10820-008-9100-6
19.
Simon
,
H. A.
,
2013
,
Administrative Behavior
,
Simon and Schuster
,
New York, NY
.
20.
Adams
,
B. L.
,
Kalidindi
,
S.
, and
Fullwood
,
D. T.
,
2013
,
Microstructure-Sensitive Design for Performance Optimization
,
Butterworth-Heinemann
,
Waltham, MA
.
21.
Kalidindi
,
S. R.
,
Niezgoda
,
S. R.
,
Landi
,
G.
,
Vachhani
,
S.
, and
Fast
,
T.
,
2010
, “
A Novel Framework for Building Materials Knowledge Systems
,”
Computers, Materials & Continua
,
17
(
2
), pp.
103
125
.
22.
Kalidindi
,
S. R.
,
Niezgoda
,
S. R.
, and
Salem
,
A. A.
,
2011
, “
Microstructure Informatics Using Higher-Order Statistics and Efficient Data-Mining Protocols
,”
JOM
,
63
(
4
), pp.
34
41
. 10.1007/s11837-011-0057-7
23.
Choi
,
H.-J.
,
Austin
,
R.
,
Allen
,
J. K.
,
McDowell
,
D. L.
,
Mistree
,
F.
, and
Benson
,
D. J.
,
2005
, “
An Approach for Robust Design of Reactive Power Metal Mixtures Based on Non-Deterministic Micro-Scale Shock Simulation
,”
J. Computer-Aided Mater. Des.
,
12
(
1
), pp.
57
85
. 10.1007/s10820-005-1056-1
24.
Choi
,
H.-J.
,
Mcdowell
,
D. L.
,
Allen
,
J. K.
, and
Mistree
,
F.
,
2008
, “
An Inductive Design Exploration Method for Hierarchical Systems Design Under Uncertainty
,”
Eng. Optim.
,
40
(
4
), pp.
287
307
. 10.1080/03052150701742201
25.
Nellippallil
,
A. B.
,
Rangaraj
,
V.
,
Gautham
,
B.
,
Singh
,
A. K.
,
Allen
,
J. K.
, and
Mistree
,
F.
,
2018
, “
An Inverse, Decision-Based Design Method for Integrated Design Exploration of Materials, Products, and Manufacturing Processes
,”
ASME J. Mech. Des.
,
140
(
11
), p.
111403
. 10.1115/1.4041050
26.
Chen
,
W.
,
Simpson
,
T. W.
,
Allen
,
J. K.
, and
Mistree
,
F.
,
1999
, “
Satisfying Ranged Sets of Design Requirements Using Design Capability Indices as Metrics
,”
Eng. Optim.
,
31
(
5
), pp.
615
619
. 10.1080/03052159908941389
27.
Majta
,
J.
,
Kuziak
,
R.
,
Pietrzyk
,
M.
, and
Krzton
,
H.
,
1996
, “
Use of the Computer Simulation to Predict Mechanical Properties of C-Mn Steel, After Thermomechanical Processing
,”
J. Mater. Process. Technol.
,
60
(
1
4
), pp.
581
588
. 10.1016/0924-0136(96)02390-4
28.
Kuziak
,
R.
,
Cheng
,
Y.-W.
,
Glowacki
,
M.
, and
Pietrzyk
,
M.
,
1997
, “
Modeling of the Microstructure and Mechanical Properties of Steels During Thermomechanical Processing
,”
NIST Technical Note (USA)
,
1393
, p.
72
. 10.6028/nist.tn.1393
29.
Gladman
,
T.
,
McIvor
,
I.
, and
Pickering
,
F.
,
1972
, “
Some Aspects of the Structure-Property Relationships in High-C Ferrite-Pearlite Steels
,”
J. Iron Steel Inst.
,
210
(
12
), pp.
916
930
.
30.
Gladman
,
T.
,
Dulieu
,
D.
, and
McIvor
,
I. D.
,
1977
, “
Structure/Property Relationships in High-Strength Micro-Alloyed Steels
,”
Proceedings of Conference on Microalloying
, ‘75, pp.
32
55
.
31.
Yada
,
H.
,
1987
, “
Prediction of Microstructural Changes and Mechanical Properties in Hot Strip Rolling
,”
International Symposium on Accelerated Cooling Rolled Steel
,
Winnipeg, MB, Canada
,
Aug. 24–25
, pp.
105
119
.
32.
Pietrzyk
,
M.
,
Cser
,
L.
, and
Lenard
,
J.
,
1999
,
Mathematical and Physical Simulation of the Properties of Hot Rolled Products
,
Elsevier
,
Kidlington, Oxford
.
33.
Phadke
,
S.
,
Pauskar
,
P.
, and
Shivpuri
,
R.
,
2004
, “
Computational Modeling of Phase Transformations and Mechanical Properties During the Cooling of Hot Rolled Rod
,”
J. Mater. Process. Technol.
,
150
(
1
), pp.
107
115
. 10.1016/j.jmatprotec.2004.01.027
34.
Taguchi
,
G.
, and
Clausing
,
D.
,
1990
, “
Robust Quality
,”
Harv. Bus. Rev.
,
68
(
1
), pp.
65
75
.
35.
Mistree
,
F.
,
Hughes
,
O. F.
, and
Bras
,
B.
,
1993
, “
Compromise Decision Support Problem and the Adaptive Linear Programming Algorithm
,”
Prog. Astronaut. Aeronaut.
,
150
, p.
251
.
36.
Nellippallil
,
A.
,
De
,
P.
,
Gupta
,
A.
,
Goyal
,
S.
, and
Singh
,
A.
,
2016
, “
Hot Rolling of a Non-Heat Treatable Aluminum Alloy: Thermo-Mechanical and Microstructure Evolution Model
,”
Trans. Indian Inst. Met.
, pp.
1
12
. 10.1007/s12666-016-0935-3
37.
Hodgson
,
P.
, and
Gibbs
,
R.
,
1992
, “
A Mathematical Model to Predict the Mechanical Properties of Hot Rolled C-Mn and Microalloyed Steels
,”
ISIJ Int.
,
32
(
12
), pp.
1329
1338
. 10.2355/isijinternational.32.1329
38.
Jägle
,
E.
,
2007
, “
Modelling of Microstructural Banding During Transformations in Steel
,”
Ph.D. dissertation
,
Department of Materials Science & Metallurgy, University of Cambridge
,
Cambridge, UK
.
39.
Jones
,
S.
, and
Bhadeshia
,
H.
,
1997
, “
Kinetics of the Simultaneous Decomposition of Austenite Into Several Transformation Products
,”
Acta Mater.
,
45
(
7
), pp.
2911
2920
. 10.1016/S1359-6454(96)00392-8
40.
Jones
,
S.
, and
Bhadeshia
,
H.
,
1997
, “
Competitive Formation of Inter- and Intragranularly Nucleated Ferrite
,”
Metall. Mater. Trans. A
,
28
(
10
), pp.
2005
2013
. 10.1007/s11661-997-0157-8
41.
Myers
,
R. H.
,
Montgomery
,
D. C.
, and
Anderson-Cook
,
C. M.
,
2016
,
Response Surface Methodology: Process and Product Optimization Using Designed Experiments
,
R. H.
Meyers
,
D. C.
Montgomery
, eds.,
A Wiley-Interscience Publications
,
Hoboken, NJ
.
42.
Mistree
,
F.
, and
Kamal
,
S.
,
1985
,
DSIDES: Decision Support in the Design of Engineering Systems
,
University of Houston
,
Houston, TX
.
43.
Nellippallil
,
A. B.
,
Song
,
K. N.
,
Goh
,
C.-H.
,
Zagade
,
P.
,
Gautham
,
B.
,
Allen
,
J. K.
, and
Mistree
,
F.
,
2017
, “
A Goal-Oriented, Sequential, Inverse Design Method for the Horizontal Integration of a Multistage Hot Rod Rolling System
,”
ASME J. Mech. Des.
,
139
(
3
), p.
031403
. 10.1115/1.4035555
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