Constrained Optimal Test Signal Design for Improved Prediction Error

This paper presents a new efficient methodology for the optimal design of discrete test signals in black-box dynamic nonlinear system identification. The approach is based on a new criterion which weights the parameter covariances with the magnitudes of output sensitivities both to reduce the parameter estimation error and also allow the optimization of the output fitness. Optimization using this criterion has a low computational cost and in the case that the regressors are well chosen the performance index approximates that of the I-optimality criterion and results in high output fitness. The new method allows for the efficient use of numerical constrained global optimization algorithms to be applied to magnitude and rate constraints on system inputs and outputs, which are essential considerations in experimental applications. The approach should thus be employable as a component of an iterative bootstrapping procedure for experimental system identification subject to safe operating limits. The approach is applied to the black-box nonlinear multiple-input multiple-output identification of an automotive engine-fueling model as a benchmark. The results are compared with those obtained by other computationally efficient methods of both nonoptimal and optimal type. Statistical validation of the results shows that the design method using the new criterion gives test signals satisfying the required operational constraints which have superior outcomes in output prediction fit.