In this talk, we are concerned the long time stability of the origin for infinite dimensional Hamiltonian systems generated by some nonlinear partial differential equations (PDEs) with inner parameter. We prove, under some nonresonant conditions which are fulfilled for most initial data, that for any integer $M\geq 3$ there exists a canonical transformation that puts the Hamiltonian into a partial Birkhoff normal form up to a reminder of order $M+1$. As a dynamical consequence, the long time stability of the origin is obtained. Finally, we take 1-dimensional nonlinear Schr$\ddot{\mbox{o}}$dinger equation with Dirichlet boundary conditions as a model problem. The technique of proof is applicable to quite general semilinear equation in one space dimension.