The diagnosis and repair of power transformer is a complicated task. It is significant for reliability and quality of power systems

esp. to where continue is required

to detect various different types of transformer as soon as possible and call for corresponding technical engineers. In this paper

sample datasets is mapped with polynomial mapping into a more higher-dimensional space

which then is used to be classified as layers. Both minimum norm classifiers subjected to minimum norm weight with small samples via higher reflects and large samples via lower reflects are investigated. The existent condition and unique solutions are obtained. It is proved that the problem of classifier solution subject to minimum norm weight and errors is equivalent to an optimization of convex linear programming

while the well-known linear theory results such as moore-penrose inverse matrices can be used to get classifier expected. For there exists measure errors in sensors or spectrometers

the robust satiability of online diagnosis systems is discussed. Finally

an example is given to illustrate our results based on dissolved oxygen analysis（DGA） and comparisons with the related research results are made.