Comment on 'a quasi-ARMAX approach to the modelling of non-linear systems' by J. Hu et al.

摘要

The paper by J. Hu et al. (2001: hereafter denoted by HKK) presents an interesting approach to the data-based modelling of non-linear stochastic systems based on neuro-fuzzy modelling concepts. As such, it reflects the massive interest in black-box modelling using network-type models that has developed over the last twenty. years and represents a good example of this genre. But the paper is also interesting because it reveals some of the limitations of such network-type models, in particular, and black-box models, in general. The purpose of this comment is to consider the only practical example presented in the paper and show how the associated data can be analysed in an alternative 'Data-Based Mechanistic' (DBM) manner that not only produces a much more efficiently parameterized model, but also provides some insight into the physical nature of the non-linearity. The aim is not to criticize the HKK paper nor the network-type models that it promotes, since these represent an undoubtedly useful approach to non-linear modelling. Rather it is to emphasize that 'neural-type' black-box models must be used with care to avoid over-parameterization, with all its attendant limitations; and to demonstrate that there are other available methods of non-linear modelling that are just as systematic and quite widely applicable. Indeed, these alternative methods may well be preferable in practical situations where the mechanistic interpretation of the model is important and a black-box model may be a deterrent to its practical application.