Design of Experiments
Why Use Design of Experiment?
With today's ever-increasing complexity of models, design of experiment has become an essential part of the modeling process. The Design Editor within the Model-Based Calibration Toolbox™ product is crucial for the efficient collection of engine data. Dyno-cell time is expensive, and the savings in time and money can be considerable when a careful experimental design takes only the most useful data. Dramatically reducing test time is growing more and more important as the number of controllable variables in more complex engines is growing. With increasing engine complexity, the test time increases exponentially.
The traditional method of collecting large quantities of data by holding each factor constant in turn until all possibilities have been tested is an approach that quickly becomes impossible as the number of factors increases. A full factorial design (that is, testing for torque at every combination of speed, load, air/fuel ratio, and exhaust gas recirculation on a direct injection gasoline engine with stratified combustion capability) is not feasible for newer engines. Simple calculation estimates that, for recently developed engines, to calibrate in the traditional way would take 99 years!
With a five-factor experiment including a multiknot spline dimension and 20 levels in each factor, the number of points in a full factorial design quickly becomes thousands, making the experiment prohibitively expensive to run. The Design Editor solves this problem by choosing a set of experimental points that allow estimation of the model with the maximum confidence using just a fraction of the number of experimental runs; for the preceding example just 100 optimally chosen runs is more than enough to fit the model. Obviously, this approach can be advantageous for any complex experimental design, not just engine research.
The Design Editor offers a systematic, rigorous approach to the data collection stage. When you plan a sequence of tests to be run on an example engine, you can base your design on engineering expertise and existing physical and analytical models. During testing, you can compare your design with the latest data and optimize the remaining tests to get maximum benefit.
The Design Editor provides prebuilt standard designs to allow a user with a minimal knowledge of the subject to quickly create experiments. You can apply engineering knowledge to define variable ranges and apply constraints to exclude impractical points. You can increase modeling sophistication by altering optimality criteria, forcing or removing specific design points, and optimally augmenting existing designs with additional points.
Design Styles
The Design Editor provides the interface for building experimental designs. You can make three different styles of design: classical, space-filling, and optimal.
Space-filling designs are better when there is low system knowledge. In cases where you are not sure what type of model is appropriate, and the constraints are uncertain, space-filling designs collect data in such as a way as to maximize coverage of the factors' ranges as quickly as possible.
Optimal designs are best for cases with high system knowledge, where previous studies have given confidence on the best type of model to be fitted, and the constraints of the system are well understood.
Classical designs (including full factorial) are very well researched and are suitable for simple regions (hypercube or sphere). Engines have complex constraints and models (high-order polynomials and splines).
You can augment any design by adding points. Working in this way allows new experiments to enhance the original, rather than simply being a second attempt to gain the necessary knowledge.
Create Examples Using the Design Editor
Follow these steps to construct space-filling, optimal, and classical designs.
Choose a model to design an experiment for, enter the Design Editor, and construct an space-filling design. Then construct and apply two different constraints to this design and view the results. Often you would design constraints before constructing a design, but for the purposes of this tutorial you make constraints last so you can view the effects on your design.
Create an optimal design.
After you create designs, use the displays and tools to examine the properties of the design, save the design, and make changes.
Create a classical design, and use the Prediction Error Variance Viewer to compare it with the optimal design. You can also use the Design Evaluation tool to view all details of any design.
