THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Statistics for Spatial Data.

Statistics For Spatial Data

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Elements Of Chemical Reaction Engineering

A paradigm for data-driven predictive modeling using field inversion and machine learning

To use predictive models in engineering design of physical systems, one should first quantify the model uncertainty via model updating techniques employing both simulation and experimental data. While calibration is often used to tune unknown calibration parameters of a computer model, the addition of a discrepancy function has been used to capture model discrepancy due to underlying missing physics, numerical approximations, and other inaccuracies of the computer model that would exist even if all calibration parameters are known. One of the main challenges in model updating is the difficulty in distinguishing between the effects of calibration parameters versus model discrepancy. We illustrate this identifiability problem with several examples, explain the mechanisms behind it, and attempt to shed light on when a system may or may not be identifiable. In some instances, identifiability is achievable under mild assumptions, whereas in other instances, it is virtually impossible. In a companion paper, we demonstrate that using multiple responses, each of which depends on a common set of calibration parameters, can substantially enhance identifiability.

Quantification of model uncertainty: Calibration, model discrepancy, and identifiability

Model validation metrics have been developed to provide a quantitative measure that characterizes the agreement between predictions and observations. In engineering design, the metrics become useful for model selection when alternative models are being considered. Additionally, the predictive capability of a computational model needs to be assessed before it is used in engineering analysis and design. Due to the various sources of uncertainties in both computer simulations and physical experiments, model validation must be conducted based on stochastic characteristics. Currently there is no unified validation metric that is widely accepted. In this paper, we present a classification of validation metrics based on their key characteristics along with a discussion of the desired features. Focusing on stochastic validation with the consideration of uncertainty in both predictions and physical experiments, four main types of metrics, namely classical hypothesis testing, Bayes factor, frequentist’s metric, and area metric, are examined to provide a better understanding of the pros and cons of each. Using mathematical examples, a set of numerical studies are designed to answer various research questions and study how sensitive these metrics are with respect to the experimental data size, the uncertainty from measurement error, and the uncertainty in unknown model parameters. The insight gained from this work provides useful guidelines for choosing the appropriate validation metric in engineering applications. [DOI: 10.1115/1.4004223]

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Toward a Better Understanding of Model Validation Metrics

Improving Identifiability in Model Calibration Using Multiple Responses

Robust design is an effective approach to design under uncertainty. Many works exist on mitigating the influence of parametric uncertainty associated with design or noise variables. However, simulation models are often computationally expensive and need to be replaced by metamodels created using limited samples. This introduces the so-called metamodeling uncertainty. Previous metamodel-based robust designs often treat a metamodel as the real model and ignore the influence of metamodeling uncertainty. In this study, we introduce a new uncertainty quantification method to evaluate the compound effect of both parametric uncertainty and metamodeling uncertainty. Then the new uncertainty quantification method is used for robust design. Simplified expressions of the response mean and variance is derived for a Kriging metamodel. Furthermore, the concept of robust design is extended for metamodel-based robust design accounting for both sources of uncertainty. To validate the benefits of our method, two mathematical examples without constraints are first illustrated. Results show that a robust design solution can be misleading without considering the metamodeling uncertainty. The proposed uncertainty quantification method for robust design is shown to be effective in mitigating the effect of metamodeling uncertainty, and the obtained solution is found to be more "robust" compared to the conventional approach. An automotive crashworthiness example, a highly expensive and non-linear problem, is used to illustrate the benefits of considering both sources of uncertainty in robust design with constraints. Results indicate that the proposed method can reduce the risk of constraint violation due to metamodel uncertainty and results in a "safer" robust solution.

Concurrent treatment of parametric uncertainty and metamodeling uncertainty in robust design

A process model for the crystallization of L-phenylalanine crystals from mixed propanol–water solution, an enantiotropic system, is developed with nucleation and growth kinetics estimated for the anhydrate and monohydrate forms using in situATR-FTIR spectroscopy and laser backscattering. A challenging aspect of estimating kinetics for this system is the formation of large numbers of small crystals under certain conditions, which result in biases in the data collected from in situATR-FTIR and FBRM probes. Batch experiments were designed to follow particular trajectories in the phase diagram so that some kinetic phenomena are suppressed in some runs, which enabled the estimation of sets of kinetic parameters in stages, reducing the number of parameters to be estimated simultaneously. The model was validated by comparison of model predictions and experiments for the product crystals and metastable limits obtained from independent characterization and experiments. This combination of experimental design and process modeling may be emulated to facilitate process modeling and development for crystallizations involving multiple crystal structures.

Paul D. Arendt

Papers

Quantification of model uncertainty: Calibration, model discrepancy, and identifiability

Toward a Better Understanding of Model Validation Metrics

Improving Identifiability in Model Calibration Using Multiple Responses

Concurrent treatment of parametric uncertainty and metamodeling uncertainty in robust design

Nucleation and growth kinetics estimation for L-phenylalanine hydrate and anhydrate crystallization