Rail welds are widely used in high-speed railways and short-wave irregularities usually appear due to limitations in welding technology. These irregularities can excite a high wheel/rail force and are regarded as the main cause of deterioration in track structures. To measure this fierce force (or deterioration of the rail weld), axle box acceleration is treated as an effective and economic measure, though an exact quantitative relation between these two quantities remains elusive. This paper aims to develop such a relation in order to provide a new theoretical basis and an analysis method for monitoring and controlling weld geometry irregularity. To better understand the characteristics of axle box acceleration, the paper consists of two parts: an observation and a numerical simulation of axle box acceleration by rail welds. Based on measured data from field tests, axle box acceleration at rail welds was found to have high-frequency vibrations in two frequency bands (i.e., 350-500 Hz and 1000-1200 Hz). Upon analyzing the vibration characteristics in time-frequency domains, the exact location of the rail weld irregularity could be identified. Subsequently, a 3D high-speed wheel/rail rolling contact finite element model was employed to investigate the effect of rail weld geometry on axle box acceleration, and led to the discovery that the weld length and depth determine the vibration frequency and amplitude of the axle box acceleration, respectively. A quantitative relation between axle box acceleration and wheel/rail force has also been determined. Finally, we propose an approach for real-time health detection of rail welds and discuss the influence of other defects and rail welds on the acceleration signal of the axle box.