Finite difference method for sensitivity analysis

I use a compressor blade as the finite element mdoel to complete sensitivity analysis. All external surface nodes are taken as design variables and K-S stress is objecitve function. After the model is symmetric along the xoz plane, the results of sensitivity analysis is different from the original results.

The left one is the results of original model, the right one is the results of symmetric model. And then FDM is used to calculate the total derivative of K-S stress with respect to design variables on the symmetric model, whose distribution is similar with the left one.

In the source codes, the finite difference method is used to compute the derivative of K-S stress with respect to design variables. As we all know that, the symbol of parameter does not affect the derivative of objective with respect to this parameter. But if I give a negative perturbation of displacements, the dgdu changed leading to the results of sensitivity analysis changing.

You can download my complete model on Data package from October 25th. -
Can you give me explanations? Thank you very much.

Best wishes.

Silly question?
¿Why do the original model has so much difference in size with the symmetric.?

There also seem to be bad shaped elements.

¿Could this negative perturbation of displacement be responsible of a negative Jacobian in some thin elements?
¿Should the negative perturbation of displacements be applied to the Symetric model or to the 180º rotated model?