Theoretically Schneider Electric's analysis does not need initial condition information. Obviously this is impossible for old transformers which are the most interesting from an ageing perspective. Schneider Electric's technique uses the reaction of the paper to temperature. The way the paper expels and absorbs moisture over any given temperature range is an indication of age. High levels of activity show young paper. Low levels show highly aged paper. Pinpointing the level of ageing requires a model of the paper. Our present predictions methodology is based on a generic (average) model of simple Kraft paper - with which we have done years of internal testing and is appropriate for old transformers. It will be important over the next years to build models for more modern enhanced transformer insulation types (TUK and glossy). We plan to start the work of expanding our model to these new papers next year through further testing in our lab.
The attached paper presented at a Chinese conference a year or two ago provides a summary explanation of the approach.