Many engineering applications, product design and optimization require
successive stages of modeling and analysis of increasing accuracy and
cost. At different stages of the design cycle, engineers need to make
use of sources of information that range from fundamental knowledge and
previous experience to detailed large-scale numerical simulations and
prototype testing. This research is developing a modeling and
experimental design strategy, called Multistage Bayesian Surrogate
Methodology (MBSM), that can integrate various forms of information to
accelerate product and process development. Using this methodology, we
build cost-effective and flexible models collecting data from different
sources through an optimal sampling strategy. We believe that having a
methodology that allows designers to create models at any desired level
of accuracy will improve the selection of initial ideas at the
conceptual design stage, decrease design cycle time, and reduce costs
Our methodology creates surrogate models using a Bayesian
framework. The surrogate is an analytical model of the expected
response for a set of design parameters. This methodology is targeted
to product or processes that are expensive to analyze, due to high
costs of the experiments or numerical simulations that are extremely
time consuming. We can integrate data information that comes from
numerical simulations as well as physical experiments, analytical
models and heuristics. This methodology does not require the assumption
of any specific form of the response; instead, models are defined in
terms of the correlation between sampling sites, assuming the response
is a realization of a stochastic process. Other approaches, such as
neural networks and response surface methodologies, can also be used to
build surrogate models. However, neural networks generally require a
large number of experiments to calibrate the response. In contrast, our
methodology is designed for situations in which the number of
experiments must be small. Response surface methodologies require a
priori assumption on the form of the response. Bayesian surrogates are
based only on the correlation between sampling points; no assumptions
about the form of the response are needed.
Surrogate models are updated and refined in successive stages. The
flow diagram below shows the flow of information for different cycles
of experimentation, modeling and analysis. At any stage, surrogate
models may be used for optimization, prediction, concurrent design,
inverse calculations, robustness studies and trade-off or sensitivity
studies. The sequential and informative updating of surrogate models
and the adaptive sampling are the main strengths of this methodology.
The figures below show a three-stage surrogate building process,
simulating data collection from an analytical test function. Data is
collected at discrete sites using a maximin array. From this data, a
first stage surrogate is built. Information from the first stage is
used to collect adaptively more data and to refine the second stage
surrogate. The procedure is repeated in a third stage for the
The main areas envisioned for the application of the MBSM are
manufacturing, product design and optimization, and process
improvement. The methodology has been successfully used to improve the
quality of parts fabricated with a novel manufacturing process called
microcasting. It has also been applied to improve steady state and
transient heat transfer performance of electronic components for
thermal design of wearable computers. Other applications have included
inverse heat transfer problems, optimization of thermal systems and
model generation for aid in the design of engineered bone tissue.
1) Weiss, L.E., Amon, C.H., Finger, S., Miller, E.D., Romero, D.A.,
Verdinelli, I. Walker, L.M., and Campbell, P.G., "Bayesian Computer-aided Experimental Design of Heterogeneous Scaffolds for Tissue Engineering," Computer Aided Design, Vol. 37, pp. 1127-1139, 2005.
2) Romero, D.A., Amon, C.H., Finger, S., Verdinelli, I., "Multi-stage Bayesian Surrogates for the Design of Time-Dependent Systems,"
Proceedings of DETC/CIE, 2004 ASME International Design Engineering
Technical Conference, DETC2004-57510, Salt Lake City, UT, 2004.
3) Pacheco, J.E., Amon, C.H. and Finger, S., "Incorporating Information from Replications into Bayesian Surrogate Models," ASME Design Theory and Methodology Conference, DETC2003/DTM-48644, Chicago, IL, 2003.
4) Pacheco, J.E., Amon, C.H., and Finger, S., "Bayesian Surrogates Applied to Conceptual Stages of the Engineering Design Process", ASME Journal of Mechanical Design, Vol. 125, pp. 664-672, 2003.
5) Romero, D.A., Amon, C.H. and Finger, S., "Modeling Time-Dependent Systems Using Multi-Stage Bayesian Surrogates," 2003 ASME International Mechanical Engineering Congress and Exposition, IMECE2003-44049, Washington D.C., 2003.
6) Pacheco, J.E., Amon, C.H., Finger, S. "Using Bayesian Models in Preliminary Design", International Design Conference - Design 2002, Dubrovnik, 2002.
7) Pacheco, J.E., Amon, C.H., and Finger, S., "Flexible Multistage Bayesian Models for Use in Conceptual Design", Proceedings of the 2002 ASME Design Theory and Methodology Conference, DETC 2002/DTM-34022, pp. 1-8, 2002.
8) Pacheco, J.E., Amon, C.H., and Finger, S., "Developing Bayesian Surrogates for Use in Preliminary Design", 2001 ASME Design Engineering Technical Conference, Theory and Methodology, ASME DETC2001/DTM-21701, 2001.
9) Leoni, N. and Amon, C.H., "Bayesian
Surrogates for Integrating Numerical, Analytical and Experimental Data:
Application to Inverse Heat Transfer in Wearable Computers", IEEE Transactions Comps. Pack. Manuf.
Technology, Vol. 23, pp. 23-33, 2000.
10) Osío, I.G. and Amon, C.H., "An Engineering Design Methodology with Bayesian Surrogates and Optimal Sampling", J. Research in Engineering Design, Vol. 8, No. 4, pp. 189-206, 1996.
For MBSM demos, click here.