Plant-Friendly Signal Generation for System Identification Using a Modified Simultaneous Perturbation Stochastic Approximation (SPSA) Methodology

摘要

The Simultaneous Perturbation Stochastic Approximation (SPSA) methodology and a modified SPSA version (MSPSA-$K$ ) were investigated for the generation of plant-friendly multisinusoidal signals. Plant-friendly properties are determined by the sinusoidal phases that are optimally selected by either the SPSA or MSPSA- $K$ algorithms. The MSPSA- $K$ methodology principally differs from SPSA in that it perturbs the signal phase parameters in $K$ subsets rather than simultaneously. Both SPSA and MSPSA-$K$ provide a flexible, extensible computational framework to incorporate various plant-friendly performance measures into the design of an input signal for experimental design purposes in system identification. In this paper, an objective function comprised of the input signal crest factor, rate of change, acceleration, and output crest factor is presented and applied to a representative case study. A detailed analysis of the tradeoffs between these various performance measures is illustrated by the selection of the weighting values for the objective function components. Using the MSPSA-$K$ method, it was found that dividing the phase parameters into two subsets resulted in better performance than simultaneously perturbing all parameters. Dividing the phase parameters into four subsets, however, did not provide any significant additional benefit. The proposed method can be applied to signals with an arbitrarily defined spectrum (in both amplitude and frequency spacing) and is easily implemented.