A method of determining stress variations over time in a fluid transport undersea pipe and providing a bottom-to-surface connection or a connection between two floating supports, the stress variations being suitable for deducing the movements, the deformations, the fatigue, and the vortex induced vibration of the pipe, the method comprising: installing along the entire length of the pipe at least one distributed optical fiber sensor (2-1 to 2-4) using Rayleigh backscattering, the sensor being dedicated to measuring at least one degree of freedom of movement variation over time of the pipe in each cross section of the pipe; continuously measuring the stress variations of the optical fiber sensor over time; characterised in that it further comprises determining deformations over time at each point of the pipe by time integration of the stress variation of the optical fiber sensor on the basis of the following matrix relationship: ∂ t ε s → = A s ∂ t x s → in which: s is the curvilinear abscissa of the fiber; ∂ t ∈(s) is a vector of dimension 1 to 6, in which the components correspond to the time derivatives of the respective axial local deformations of the optical fiber sensors; ∂ t x ( s) is a vector having the same dimension as ∂ t ∈(s) representing the time derivatives of the deformation reduction elements at the center of gravity of the structure section corresponding to the curvilinear abscissa s for measuring on the pipe; and A(s) is a deformation matrix that is a function of the local positions and angular orientations of the optical fiber sensors on the pipe, of the curvilinear abscissa s, and of the mechanical and geometrical properties of the structure, the optical fiber sensors being installed in such a manner that the deformation matrix A(s) is invertible. installing along the entire length of the pipe at least one distributed optical fiber sensor (2-1 to 2-4) using Rayleigh backscattering, the sensor being dedicated to measuring at least one degree of freedom of movement variation over time of the pipe in each cross section of the pipe; continuously measuring the stress variations of the optical fiber sensor over time; characterised in that it further comprises determining deformations over time at each point of the pipe by time integration of the stress variation of the optical fiber sensor on the basis of the following matrix relationship: ∂ t ε s → = A s ∂ t x s → in which: s is the curvilinear abscissa of the fiber; ∂ t ∈(s) is a vector of dimension 1 to 6, in which the components correspond to the time derivatives of the respective axial local deformations of the optical fiber sensors; ∂ t x ( s) is a vector having the same dimension as ∂ t ∈(s) representing the time derivatives of the deformation reduction elements at the center of gravity of the structure section corresponding to the curvilinear abscissa s for measuring on the pipe; and A(s) is a deformation matrix that is a function of the local positions and angular orientations of the optical fiber sensors on the pipe, of the curvilinear abscissa s, and of the mechanical and geometrical properties of the structure, the optical fiber sensors being installed in such a manner that the deformation matrix A(s) is invertible. s is the curvilinear abscissa of the fiber; ∂ t ∈(s) is a vector of dimension 1 to 6, in which the components correspond to the time derivatives of the respective axial local deformations of the optical fiber sensors; ∂ t x ( s) is a vector having the same dimension as ∂ t ∈(s) representing the time derivatives of the deformation reduction elements at the center of gravity of the structure section corresponding to the curvilinear abscissa s for measuring on the pipe; and A(s) is a deformation matrix that is a function of the local positions and angular orientations of the optical fiber sensors on the pipe, of the curvilinear abscissa s, and of the mechanical and geometrical properties of the structure, the optical fiber sensors being installed in such a manner that the deformation matrix A(s) is invertible.