Nonlinear restoring forces have been widely introduced into the harvesting of vibratory energy to enhance energy harvester performance. Generally, the various source of nonlinearity include magnetic forces, spring forces, geometric and material nonlinearity, etc. However, these kind of nonlinear forces cannot be manipulated in an arbitrary manner. The performance of the energy harvester can be further optimized if the nonlinear forces are manipulated according to the requirements. The aim of this work is to study the energy harvesting performance of vibration energy harvester that can customize the nonlinear forces subjected to Gaussian white noise. The approximate analytical solution is obtained by moment differential method for the vibration energy harvester and there is a good agreement between analytical and the numerical solution obtained by Euler Maruyama scheme. Mean squared output power is presented to illustrate the device output performance. The nonlinear forces are customized For monostable and bistable piezoelectric energy harvester and the influence of noise intensity, and effect of system parameters on the response of the energy harvester is analyzed both numerically and analytically. The effect of stochastic resonance on the performance of the system also analyzed numerically for the bistable energy harvester.