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Vehicle vibration is one of the most critical issues hindering the supply of attractive automobiles to customers. This study focuses on drivability related to longitudinal vehicle body vibration excited by driver input at tip-in acceleration. To understand and design the vibration, a physical model with necessary and sufficient fidelity for its reproduction is required. Moreover, estimation of the excitation input (control input) is also vital for this reproduction. However, achieving both the accurate measurement and modeling of the control input is difficult and labor intensive. Therefore, a novel low-order physical modeling approach with control input estimation using operational output-only measurement is proposed here. The proposed approach requires some assumptions, such as inertia information, but requires no input measurement, no preliminary testing, no limitation to a linear model, and no assumptions in estimating the control input. The basic concept is to regard the vehicle system as a relationship (called a vibration transfer structure) between rigid-body motions and restoring forces and moments (called transfer forces). The proposed approach is implemented in five steps: First, the operational output is measured during tip-in acceleration. Second, important motions are extracted from the output using tensor decomposition. Third, a simplified transfer structure is determined using the important motions. Fourth, the control input and the transfer forces are estimated as time-series data using the structure. Finally, by characterizing the transfer forces, a low-order physical dynamic model is obtained. The effectiveness of this approach is demonstrated using two sets of operational tip-in acceleration data. • This paper proposes a novel modeling approach for automotive vehicle vibrations. • It simplifies modeling of various vehicles by only requiring operational output data. • It constructs a low-order physical model, which is not limited to linearity. • It estimates operational control input signal required for reproducing vehicle vibration. • It incorporates PARAFAC decomposition and a model order selection method is proposed. [ABSTRACT FROM AUTHOR]