Design of experiments
 | .Introduction
For a standard design of experiments the number of experiments required for a linear approximation increases exponentially with the number of inputs. When one is using the experimental approach for parameter design (or design for robustness) the number of experiments required is even higher again. With just a typical number of inputs the number of required experiments can be considerable. This can mean a significant (and sometime prohibitive) demand upon resources and time. Design of experiments To reduce this demand upon resources the effective number of input variables needs to be reduced. Dimensional analysis and design of experiments Dimensional analysis is an established method of partially solving for the relationship between the inputs and the outputs of a system that is not fully understood. Sometimes, dimensional analysis can solve for so much of the relationship between the input and the output that only one experiment is needed to fully define that relationship. Under such conditions, design of experiments is no longer required; standard analytical robustness techniques can be used. How dimensional analysis helps If dimensional analysis design of experimentssn't come close to completely solving for the relationship between inputs and output, then it will at least significantly reduce the effective number of input variables by identifying dimensionless groups (sometimes called pie groups). After dimensional analysis, when applying design of experiments the dimensionless numbers are treated as input variables instead of the actual input variables themselves. Because there are fewer dimensionless groups than input variables, there will a much reduced number of required experiments (and much less workload). Performing design of experiments after dimensional analysis When using dimensional analysis with design of experiments it is important that the right constituent variables (the original input variables that now make up the dimensionless groups) to adjust. Do not use constituent variables that are shared by two or more dimensionless groups. If this is done, then it will not be possible to properly assess the contribution of each dimensionless group to the output. Dimensional analysis, design of experiments and analytical methods An alternative to experimental optimisation or robustification is to actually perform enough experiments to create and accurate empirical relationship between the dimensionless groups and the output. Because the effective number of inputs is reduced, this is often a viable option. With such an accurate model, it is possible to apply standard robustification techniques suited to an analytical model. This can significantly reduce the time required to robustify the system and the results will be far more accurate. Summary By combining dimensional analysis with design of experiments it is possible to partially solve for the relationship between the inputs and the outputs. This in turn can make optimisations such as robustification much faster and much more accurate. Either by effectively reducing the number of inputs or allowing for the easy development of an accurate empirical model suited to analytical methods. Design of experiments |
