The monitored sections are always assembled behind working face excavation. The displacement induced during this period is called loss displacement. The optimization back analysis method is used to get loss displacement. The method transforms the problem to a global optimized problem that treats the error between geodesic loss displacement and computational loss displacement as objective function

the mechanical parameters of surrounding rocks as decision variables. Aiming to solve the global optimized problem that is high nonlinearity

many peak values and expensive cost

an intelligent cooperative optimization algorithm based on particle swarm optimization (PSO) and Gaussian process (GP) machine learning for back analysis is proposed

then combined the FLAC3D

a new method called PSO-GP-FLAC3D for the loss displacement back analysis is developed. The results of a numerical example show that the proposed method is feasible. It not only obtains reliably predicted loss displacement

but also gets reasonable mechanical parameters of surrounding rocks. In addition

the proposed method has the merits of global optimization and high computational efficiency. It can overcome the shortcomings that the traditional optimization back analysis method is easy to fall into local optimum or overly dependent on initial learning samples. The proposed method is applied to the auxiliary tunnel BK14+599 section of Jinping Ⅱ hydropower station in China

and loss displacement and mechanical parameters of surrounding rocks are obtained. The results indicate that the elastic deformation of surrounding rocks increased quickly after excavation

which results in large loss displacement. Therefore

the loss displacement of surrounding rocks can not be ignored in stability evaluation or back analysis for underground engineering

especially for deep underground rock engineering.