Thermography spatial-transient-stage mathematical tensor construction and material property variation track

•Characterizing and tracking the properties variation use eddy current pulsed thermography.•spatial-transient-stage tensor mathematical model.•Tucker decomposition is developed to track the properties variation of the material.•Simulation and real experiment of gears with fatigue tests is evaluated.

Characterizing and tracking the properties variation in conductive material such as electrical conductivity, magnetic permeability and thermal conductivity have promising potential for the detection and evaluation of material state undertaken by fatigue or residual stress. This is a challenge task for the research field of non-destructive testing and evaluation. This paper proposes a spatial-transient-stage tensor mathematical model of inductive thermography system and Tucker decomposition algorithm for characterizing and tracking the variation of properties. The inductive thermography has advantages in such as rapid inspection and high sensitivity of defect detection. The links between mathematical and physics models have been discussed. The simulation experiments of tracking physic properties of steel material are investigated and verified. In addition, the real experiment of the measurement for gears with different cycles of fatigue tests is evaluated. The estimation of normalized stage basis by using Tucker decomposition has shown high correlation relationships with different variation of physics properties in material.