Model uncertainty often results from incomplete system knowledge or simplification made at the design stage. In this paper, a hybrid model/data-based probabilistic design approach is proposed to design a nonlinear system to be robust under the circumstances of parameter variation and model uncertainty. First, the system is formulated under a linear structure which will serve as a nominal model of the system. All model uncertainties and nonlinearities will be placed under a sensitivity matrix with its bound estimated from process data. On this basis, a model-based robust design method is developed to minimize the influence of parameter variation in relation to performance covariance. Since this proposed design approach possesses both merits from the model-based robust design as well as from the data-based uncertainty compensation, it can effectively achieve robustness for partially unknown nonlinear systems. Finally, two practical examples demonstrate and confirm the effectiveness of the proposed method.

References

References
1.
Caro
,
S.
,
Bennis
,
F.
, and
Wenger
,
P.
, 2005, “
Tolerance Synthesis of Mechanisms: A Robust Design Approach
,”
J. Mech. Des.
,
127
(
1
), pp.
86
94
.
2.
Lu
,
X. J.
,
Li
,
H. X.
, and
Chen
,
C. L.
, 2010, “
Variable Sensitivity Based Deterministic Robust Design for Nonlinear System
,”
J. Mech. Des.
,
132
(
6
), p.
064502
.
3.
Ting
,
K. L.
, and
Long
,
Y. F.
, 1996, “
Performance Quality and Tolerance Sensitivity of Mechanisms
,”
J. Mech. Des.
,
118
(
1
), pp.
144
150
.
4.
Zhu
,
J. M.
, and
Ting
,
K. L.
, 2001, “
Performance Distribution Analysis and Robust Design
,”
J. Mech. Des.
,
123
(
1
), pp.
11
17
.
5.
Parkinson
,
A.
, 1995, “
Robust Mechanical Design Using Engineering Models
,”
J. Mech. Des.
,
117
, pp.
48
54
.
6.
Du
,
X. P.
, and
Chen
,
W.
, 2000, “
Towards a Better Understanding of Modeling Feasibility Robustness in Engineering Design
,”
J. Mech. Des.
,
122
(
4
), pp.
385
393
.
7.
Al-Widyan
,
K.
, and
Angeles
,
J.
, 2005, “
A Model-Based Formulation of Robust Design
,”
J. Mech. Des.
,
127
(
3
), pp.
388
396
.
8.
Kalsi
,
M.
,
Hacker
,
K.
, and
Lewis
,
K.
, 2001, “
A Comprehensive Robust Design Approach for Decision Trade-Offs in Complex Systems Design
,”
J. Mech. Des.
,
123
(
1
), pp.
1
9
.
9.
Li
,
M.
,
Azarm
,
S.
, and
Boyars
,
A.
, 2006, “
A New Deterministic Approach Using Sensitivity Region Measures for Multi-Objective Robust and Feasibility Robust Design Optimization
,”
J. Mech. Des.
,
128
, pp.
874
883
.
10.
Gunawan
,
S.
, and
Azarm
,
S.
, 2005, “
A Feasibility Robust Optimization Method Using Sensitivity Region Concept
,”
J. Mech. Des.
,
127
, pp.
858
865
.
11.
Gunawan
,
S.
, and
Azarm
,
S.
, 2005, “
Multi-Objective Robust Optimization Using a Sensitivity Region Concept
,”
Struct. Multidiscip. Optim.
,
29
(
1
), pp.
50
60
.
12.
Lu
,
X. J.
, and
Li
,
H. X.
, 2009, “
Perturbation Theory Based Robust Design for Model Uncertainty
,”
J. Mech. Des.
,
131
(
11
), p.
111006
.
13.
Chen
,
W.
,
Allen
,
J. K.
,
Tsui
,
K. L.
, and
Mistree
,
F.
, 1996, “
A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors
,”
J. Mech. Des.
,
118
(
4
), pp.
478
493
.
14.
Choi
,
H. J.
, and
Allen
,
J. K.
, 2009, “
A Metamodeling Approach for Uncertainty Analysis of Nondeterministic Systems
,”
J. Mech. Des.
,
131
(
4
), p.
041008
.
15.
Lee
,
Y.
, and
Nelder
,
J. A.
, 2003, “
Robust Design via Generalized Linear Models
,”
J. Quality Technol.
,
35
(
1
), pp.
2
12
.
16.
Nair
,
V. N.
,
Taam
,
W.
, and
Ye
,
K. Q.
, 2002, “
Analysis of Functional Responses From Robust Design Studies
,”
J. Quality Technol.
,
34
(
4
), pp.
355
370
.
17.
Sohn
,
S. Y.
, and
Park
,
C. J.
, 1998, “
Random Effects Linear Models for Process Mean and Variance
,”
J. Quality Technol.
,
30
(
1
), pp.
33
39
.
18.
Ljung
,
J.
, 1987,
System Identification: Theory for the User
,
1st ed.
,
Prentice Hall
,
Englewood Cliffs, NJ
.
19.
Sandoval
,
L. A. R.
,
Budman
,
H. M.
, and
Douglas
P. L.
, 2008, “
Simultaneous Design and Control of Processes Under Uncertainty: A Robust Modeling Approach
,”
J. Process Control
,
18
, pp.
735
752
.
20.
Stewart
,
G. W.
, and
Sun
,
J. G.
, 1990,
Matrix Perturbation Theory
,
Academic Press
,
Boston
.
21.
Ralph
,
B.
, and
Stephen
,
G. N.
, 1989, “
Approaches to Robust Pole Assignment
,”
Int. J. Control
,
49
(
1
), pp.
97
117
.
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