151st ASA Meeting, Providence, RI

Adaptive Mechanical Model of Human Footsteps

Alexander Ekimov - aekimov@olemiss.edu
James M. Sabatier
NCPA, University of Mississippi
University, MS 38677

Popular version of paper 4aSAb1
Presented Thursday Morning, June 8, 2006
151st ASA Meeting, Providence, RI

The vibration signature from footsteps can be exploited for recognizing and characterizing human intruders. From an engineering point of view, footsteps are repeatable cycles of supported surface loading by a dynamic force. This force produces the vibration response of the ground or floor starting from frequencies less than one Hz up to ultrasonic frequencies.


Figure 1. Serial frames of the video record of a single footstep and corresponding them the spectrogram of the acceleration

The footstep force is due to two components: the force perpendicular (normal) to the surface and the force tangential to the surface. The magnitude of the normal force component depends on the kind of human motion (e.g., walking, running, etc.) and on the persons weight. For example, the normal force component is approximately equal to the persons weight for a typical walking style. We break down the complex acoustic signal from a footstep into a spectrum of frequencies, by representing the acoustical signal as a combination of different sine waves each with a single frequency (this is called Fourier analysis). As a result, the average value of the normal force from footsteps produces a maximum Fourier component that is concentrated between 1-4 Hz, below the range of human hearing. The normal force component generates the low-frequency vibrations (typically below 500 Hz) that are currently used for intruder detection by seismic methods. The tangential force is governed by the horizontal motion and is equal to the friction force. The interactions of foot and the ground/floor produce sliding contacts and result in broadband frequency vibrations and sound.

The vibration response at the distance R from the applied force is proportional to the dynamic force and results from the product of the footstep force and the ground/floor specific transfer function. The transfer function describes the propagation of vibration between the force location and the location of the detector. The vibration response of the ground/floor to the footsteps depends on the manner of walking or style as well too. Stealthy walking is undetectable at even a few meters from a seismic sensor.

Walkers could vary the normal component of dynamic force of footsteps by controlling leg stiffness and as a result vary the vibration response of the ground/floor. An adaptive model of a walking person as a mass-spring system with controlled leg-spring stiffness was developed. This model explains the algorithm of walking stealthy.

Three distinct types of walking styles (regular, soft, and stealthy) with the same speed of motion were described and investigated.


Figure 2. Time domain signal and spectrogram of a single footstep for regular, soft and stealthy styles of walking.
Video files: regular, soft, and stealthy.

These styles result in different vibration magnitudes in the low-frequency range (below 100 Hz) due to differences in the walkers leg stiffness and as a result in variation of distances for the footstep vibration response detection.


Table 1. Average value of acceleration

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