For the ill-posed problem in aero-engine gas path diagnosis that the amount of measuring parameters is less than the amount of parameters to be measured

considering the uncertainty of both the measuring parameters and the theoretic model component characteristics

a fault diagnostic algorithm called variational weighed least squares was built using engine counterbalance technology and non-linear mathematical model. The algorithm was applied to an engine fault diagnosis. The results show that the difference between the measurements and calculation results can be obtained with the algorithm. At the same time

through modifying the original mathematical model by employing fault parameter corrections

the thrust maximum deviation between the calculation and measurement decreases from 8.25% to 1.66%

and the maximum deviation of fuel consumption rate from 6.25% to 1.50%.