The monitoring of overhead contact lines (OCL) is a key part of railway infrastructure maintenance. This paper proposes a methodology to assess the lateral geometry of contact wire, the so-called stagger, by using the dynamic response of a pantograph. The methodology is tested in a validated virtual environment that resembles the behaviour of the pantograph when it interacts with the OCL. A signal processing is developed to define features relating the lateral position of the contact wire with the vertical acceleration of the contact strip. It is demonstrated that these features have a clear and close connection with the lateral position of the contact wire. Subsequently, model-driven machine learning algorithms are defined using these features to address the OCL stagger prediction and the detection of out-of-range lateral displacement due to a faulty steady-arm. The methodology shows a good prediction performance in the estimation of the stagger amplitude/central position and the steady-arms diagnosis. The prediction of the stagger amplitude is performed with a root-mean-square error of 4.7(10) mm. In addition, the area under the Precision-Recall curve is 0.952 CI95 [0.940, 0.962] for the steady-arms diagnosis.