Orthogonal Matrices Sample Clauses

Orthogonal Matrices. Orthogonal Matrices, also referred to as Taguchi Tables, is a method for assessing the effect of parameter variables on objective values without having to explore the entire design space. Key to the concept of orthogonal matrices is the idea of parameters inter- actions. The idea is that the performance of a design is very likely not dependant on the values of individual parameter but actually is dependant on the set of all values acting in concert. To see the results of all inter- actions it is necessary to simulate every permutation of design parameters, which is identical to performing an exhaustive search described previously. At the other end of the interaction scale it is possible to ignore the effects of parameters interactions and performing sufficient simulations so that each parameter value is simulated at least once. An orthogonal matrix then is a compromise between an exhaustive search and only simulating with each parameter value only once, and the compromise is in terms of how many parameters are included in each interaction, larger numbers of parameters included in each interaction means more simulations need to be performed to see their effects and conversely small numbers of parameters included in each interaction requires fewer simulations. An orthogonal matrix defines, for a given number of parameters each with a set of possible values and for a defined interaction size (minimum 2), exactly what simulations need to be performed so that each interaction is simulated at least once. For example, if a design has three parameters, A, B and C each with their own set of values, then a matrix considering interactions of size 2 would include all combina- tions of the parameters A and B and also also combinations of parameters of A and C. The results are analysed as a set of graphs, Fig. 1, where each graph plots the objective value against the values of a particular parameter or group of parameters, and from these graphs it is possible to estimate the best values or range of values for each parameter, then the simulations confirming the predictions of the graphs may be performed. Key to building an orthogonal Better Worse v1 v2 v3 (a) v1 v2 v3 (b) v1 v2 v3 (c) Figure 1: Simple example graph results from the Orthogonal Matrices method. matrix is specifying the order of interactions that are to be considered. The smallest orthogonal matrices only consider the interactions of pairs of pa- rameters and the largest matrix would consider all interactio...
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