60 K. Worden et al. an adaptive solver like the .4;5/th-order Runge–Kutta method for the solution of non-stiff problems encapsulated in the Matlab function ode45; however, it was shown in [16] that the use of the adaptive scheme in the context of evolutionary system identification can lead to strange results. The excitations for the predictions were established by the measured base accelerations Ry0 and the initial estimate m . Although a great deal of data were measured in the experiments, the SADE identification scheme is computationally expensive, with the main overhead associated with integrating trial equations forward in time. For this reason, the training set or identification set used here was composed of only N D700 points. To avoid problems associated with transients, the cost function was only evaluated from the final 500 points of each predicted record. Once the data were generated, the SADE algorithm was applied to the identification problem using a parameter vector . The standard DE algorithm of reference [11] attempts to transform a randomly generated initial population of parameter vectors into an optimal solution through repeated cycles of evolutionary operations, in this case: mutation, crossover and selection. In order to assess the suitability of a certain solution, the cost function referred to above was used; this casts the identification in the form of a minimisation problem. Figure 7.3 shows a schematic for the procedure for evolving between populations. The following process is repeated with each vector within the current population being taken as a target vector; each of these vectors has an associated cost J defined above. Each target vector is pitted against a trial vector in a selection process which results in the vector with lowest cost advancing to the next generation. The process for constructing the trial vector involves variants of the standard evolutionary operators: mutation and crossover. + + F CROSSOVER TRIAL VECTOR SELECTION MUTATION CURRENT POPULATION POPULATION FOR NEXT GENERATION TARGET VECTOR Two Randomly Chosen Vectors Combined To Form A Scaled Difference Vector 35 35 COST VALUE Third Randomly Chosen Vector Added To Scaled Difference Vector - + 46 92 13 21 102 22 9 23 73 95 Fig. 7.3 Schematic for the standard differential evolution algorithm
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