Multistage Bayesian

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 in optimization.

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 surrogate.

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.

Recent Publications

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.