# A note about the difference in models for diagnostics and prognostics – ICSL

It is worthwhile to note that, in general, it is likely that the system’s model used in the diagnosis task will not be the same as the model used in the prognosis task. The reason for this is that models usually replicate a predetermined set of system characteristics while assuming that others are constant, and the two sets generally differ in diagnoses and prognoses. This assumption allows for models to be kept as simple as our tolerances require. Unnecessary model complexity is, naturally, typically avoided because a model that simulates unneeded and negligible conditions can require excessive work, solution time and computing power, and on top of this, there is the danger of unaccounted-for behaviors, unexplained deviations and, perhaps counter-intuitively, even loss of accuracy, since the expanded set of parameters (away from those of interest) may not be as well known.

Take, for example, the case of a geared transmission with a crack in a component. The diagnosis model attempts to reproduce signals corresponding to specific crack lengths in the transmission, one crack length at a time. Information on how the crack grows is irrelevant for this model. This progression is not considered, and, as a matter of fact, the damage may be assumed static for each simulation run of the diagnosis model.

On the other hand, for prognosticating the crack growth we need a different kind of model, one that gives information about how the crack length progresses in time. Damage is not static anymore, and, as a matter of fact, monitoring signals need not even be considered here, since they are an effect of the crack length, and not the focus of the progression study, which is concern only with its causes. The prognostics model should be able to simulate the progression of the crack length and consider the degradation of the system due to the development of damage and the variations in loading of the gearbox (i.e., usage patterns). Furthermore, these states of the system may not be accurately known. Even after performing diagnostics of the system, we can only approximate the crack length at any given instant, and the load to be experienced by the cracked component will also be an estimate, better expressed stochastically. Both of these states will be most properly described with probability distributions. And because of this, our fault progression model ought to render probabilistic results as well.