<p>A bi-material topology optimization approach is developed to minimize the integration of non-negative intensity (NNI) on predefined surfaces. NNI provides a surface field on the radiating structure that consists solely of positive contributions to the radiated sound power. The fast multipole method (FMM) is adopted for NNI evaluation by solving the eigenvalues of the symmetric acoustic impedance matrix using a two-stage solution procedure to intuitively characterize the contribution of structural surfaces to far-field radiation. FMM is further employed to effectively transform the key operators for the solution of adjoint equations, thus enabling the rapid computation of sensitivity adjoint problems and improving the total efficiency of topology optimization for large-scale vibro-acoustic coupled systems. Bi-material topology optimization with the NNI integral over a predefined region as the objective function can effectively alter the acoustic radiation pattern of a coupled system, reduce the contribution of the radiating heat zone to far-field sound radiation, and simultaneously decrease the structural radiated sound power. Numerical results demonstrate the effectiveness of the proposed optimization method in minimizing the integration of non-negative intensity.</p>