Model validation by the distortion method: linear state space systems

The distortion method was introduced by Butterfield and Thomas (1986) as a means of verifying a nominal system model, comprising a set of ordinary, nonlinear differential equations, by comparing the model response with a set of experimentally obtained data. The essence of the method is to make the minimum distortions to the model parameters necessary to ensure that the model output exactly matches the measured data. The distortions thus obtained can then be tested against a priori knowledge of the parameters, in particular to see if the variance of the distortions is less than the uncertainty in the expected parameter values. In the paper it is shown that, if the nominal model is linear, then, under certain conditions, explicit formulas can be obtained for the distortions, or significant simplifications can be made to the equations, thus removing or reducing the considerable computational overhead inherent in the method. The results of the paper could find application not only in the area of linear modelling (for example in compartmental modelling) but also in model reduction and linearisation, where the method offers a means of testing the validity of the linear or reduced-order model.