With the development of internet of things technology, smart water conservancy has become a trend in the field of water conservancy. In recent years, the advancement of image restoration technology and machine learning has expanded the acquisition and prediction of information in the meteorological and hydrological fields, promoting the progress of intelligent research on the stability monitoring of water conservancy engineering cofferdams. Due to the efficiency, stability, and low storage requirements of the conjugate gradient method, it has been widely applied in the fields of image restoration and machine learning. This paper proposes a modified HZ (MHZ) conjugate gradient method, which possesses sufficient descent and trust region properties without being constrained by line search rules. The MHZ method establishes global convergence under the modified WWP (MWWP) line search and successfully solves problems in image restoration and machine learning. Through comparison with other existing mainstream methods, it is concluded that the MHZ algorithm demonstrates superior numerical performance. This research outcome can provide relevant basis for further studies in the field of hydraulic cofferdam safety.