A Simple Method for Processing Measurements of Vehicle 

Response to Underbody Blast during Live Fire Test 

and Evaluation

by Robert J Spink

ARL-TR-7030 August 2014

Approved for public release; distribution is unlimited.
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Army Research Laboratory

Aberdeen Proving Ground, MD 21005-5068

ARL-TR-7030 August 2014

A Simple Method for Processing Measurements of Vehicle 

Response to Underbody Blast during Live Fire Test 

and Evaluation

Robert J Spink

Warrior Injury Assessment Manikin Project Management Office, ARL

Approved for public release; distribution is unlimited.
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A Simple Method for Processing Measurements of Vehicle Response to 

Underbody Blast during Live Fire Test and Evaluation

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Robert J Spink

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14. ABSTRACT

As part of the Live Fire Test and Evaluation process, military vehicles for ground combat are tested against under-body threats 

like those recently used against Soldiers in Iraq and Afghanistan. In many cases, accelerometers are used to measure the 

structural response of these vehicles. The resulting data can then be used to characterize the environment of a mounted occupant 

in these blast events. However, it must first be processed in a robust and repeatable way to yield metrics that are relatively 

insensitive to nuances of data collection such as sample rate and anti-alias filtering. This report details one such method with 4

steps that produce values for peak velocity of a constitutive accelerometer record and the time taken to achieve this peak 

velocity. A MATLAB implementation of the method is also provided in the Appendix to the report.

15. SUBJECT TERMS

LFT&E, vehicle, structure, accelerometer, data

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iii

Contents

Contents iii

List of Figures iv

Acknowledgments v

1. Background 1

2. Methodology 4

2.1 Calculation Method .........................................................................................................4

2.1.1 Step 1 – Baseline Shifts......................................................................................4

2.1.2 Step 2 – Locate the Peak ....................................................................................5

2.1.3 Step 3 – Calculate Velocity Slope......................................................................6

2.1.4 Step 4 – Calculate Time-to-Peak........................................................................8

3. Conclusion 9

4. References 10

Appendix. MATLAB Script for Calculating Peak and Time-to-Peak Velocities 11

List of Symbols, Abbreviations, and Acronyms 13

Distribution List 14
iv

List of Figures

Fig. 1 The contrived response of a test article exposed to a blast event........................................1

Fig. 2 Acceleration measured with 100 kHz and 20 kHz sample rates .........................................2

Fig. 3 Velocity from the actual acceleration data (black), 100 kHz sampled data (red), and 

20 kHz sampled data (blue) .......................................................................................................3

Fig. 4 Acceleration and velocity from the original (red) and baseline shifted (black) data ..........5

Fig. 5 The absolute (red) and final (blue) peak velocities .............................................................6

Fig. 6 Velocity slope from 5% (blue) to 95% (red) of the final peak velocity ..............................7

Fig. 7 Velocity slope from 5% (blue) of the difference between the final peak velocity and 

the point after the last negative derivative (green) to 95% (red) of the difference between 

the final peak velocity and zero .................................................................................................8

Fig. 8 The full approximation of the rise in velocity formed by extending (blue) the velocity 

slope (red) developed in Step 3..................................................................................................9
v

Acknowledgments

The author would like to acknowledge and thank Jason Tice, Brian Minch, Brian Benesch, and 

Vesta Bateman for their technical contributions to the method described in this report.
vi

INTENTIONALLY LEFT BLANK.
1

1. Background

When testing the performance of vehicles against under-body threats such as those used in Iraq 

and Afghanistan, the response of a vehicle’s structure is measured, in part, with accelerometers.

Specifically, measurements are taken from the seats and floor as these locations are in direct 

contact with the occupant and thus give some insight into the loading condition experienced. 

This structural-response data can be combined with measurements taken from anthropomorphic 

test devices placed at crew positions to provide valuable information regarding the interaction 

between vehicle’s components and occupants. These data can be used to characterize the 

environment that the mounted occupant is exposed to and inform changes to the design of 

vehicular components to enhance crew survivability.

Drawing insights from accelerometer data is not necessarily intuitive as the quantitative and 

qualitative characteristics of the data are largely influenced by their measured frequency content. 

This content, not readily discernible through visual inspection, is influenced by sample rate and 

the need to prevent aliasing by implementing hardware filters.

This point is illustrated with a simplified example of a test article exposed to a blast event. The 

response of the fictitious test article, shown in Fig. 1, is composed of superimposed accelerations 

with magnitudes of 1,000 m/s2and 10,000 m/s2and frequencies of 50 Hz and 10 kHz, 

respectively. 

Fig. 1 The contrived response of a test article exposed to a blast event
2

Environments with accelerations between 300 g to 1,000,000 g and including mixed frequency 

content between 10 Hz and 1 MHz are classified as “ballistic shock” by MIL-STD-810G, a 

military standard used during Live Fire Test and Evaluation (LFT&E) tests for underbody blast.

1

Though fictional, this example meets these criteria and can therefore be considered a ballisticshock event. The measurement techniques used to characterize it should therefore include 

instrumentation with a “flat frequency response to at least 100 kHz”, a digitizing rate “at least 2.5 

times” the anti-alias (AA) filter frequency, and AA filtering that provides “an attenuation of 50 

dB or greater for frequencies that will fold back into the passband”.1The “measured”

accelerations are compared in Fig. 2, where they are sampled at 100 kHz and 20 kHz with AA 

filters of 40 kHz and 8 kHz, respectively, each simulated as digital 4-pole Butterworth filters. 

Fig. 2 Acceleration measured with 100 kHz and 20 kHz sample rates

Not surprisingly, the 8 kHz AA filter required by MIL-STD-810G with the 20 kHz sample rate 

removed the contribution of the 10 kHz acceleration while the 40 kHz AA filter required with the 

100 kHz sample rate did not. Perhaps more importantly from an assessment standpoint, the 

restriction of data bandwidth to 8 kHz reduced the peak acceleration by more than 90% as 

compared to applying the 40 kHz filter. Since it is possible for the bandwidth of LFT&E data to 

vary, this example underscores the potentially misleading nature of acceleration magnitude as a 

metric when analyzing structural data and the value of seeking alternatives.

For many researchers and analysts, velocity is an intuitive engineering parameter. As the integral 

of acceleration, it is also less susceptible to the presence or absence of relatively high-frequency 

content and, therefore, is an attractive alternative to acceleration-based metrics. This is easily 

illustrated by turning back to the simple example. Velocities for the “actual” and “measured”
3

responses are given in Fig. 3. The expanded view from 9.5 to 10 milliseconds shows that the 

reduction in maximum velocity associated with the lowest sample rate is approximately 5%. 

Fig. 3 Velocity from the actual acceleration data (black), 100 kHz 

sampled data (red), and 20 kHz sampled data (blue)

Not only is the assessed structural velocity less sensitive to the nature of the data and how they 

were captured, the use of peak velocity as a metric for vehicle response is useful from an 

occupant-injury perspective due to the known velocity-dependent nature of human tissue.

2, 3

 

However, since tissue has the characteristic of dissipating energy over time, it is also useful to 

know how quickly the assessed peak velocity is achieved. The ratio of the peak velocity to the 

time-to-peak velocity provides a constant pseudo-acceleration, albeit one much less susceptible 

to the effects of sampling and filtering. 

To benefit from any metric, it is imperative that it be assessed in a uniform manner whether 

analyzing large amounts of data or making comparisons between test events. So it is, too, for the 

calculation of peak velocity and time-to-peak velocity. To achieve the goal of calculating these 

parameters uniformly, a codified and automated process should exist that is applicable to as 

many valid structural responses as possible. One such process is described in the next section 

with an example and provided in the form of a MATLAB script in the Appendix.
4

2. Methodology

2.1 Calculation Method

The following steps detail a simple method for calculating peak velocity and time-to-peak 

velocity from an acceleration record. The first step is to apply baseline shifts to the acceleration 

data. Following integration, the appropriate peak velocity is identified. The slope of the velocity 

rise is then calculated and used to determine time-to-peak velocity. Issues such as rotation of the 

test article, time misalignment, aliasing, clipping, and other data-acquisition issues are not 

addressed here but should be avoided and, if possible, reconciled prior to the implementation of 

this method.

2.1.1 Step 1 – Baseline Shifts

Two distinct baseline adjustments are made to the acceleration record prior to integration. In the 

first, the mean pre-trigger acceleration is subtracted from the entire data record to remove any 

systemic baseline shift. If the test article comes to rest prior to the end of the data record, a 

second baseline adjustment is applied in which the average post-trigger acceleration is subtracted 

from the post-trigger data record in order to remove any residual velocity.

4

If a non-zero velocity 

is present in the test article at the end of the data record, the second baseline adjustment should 

not be applied. As Fig. 4 shows, these shifts do not noticeably alter the acceleration record but 

provide a meaningful correction to the velocity trace. This correction is small at early times in 

the velocity record but more substantial at later times due to the accumulation of error when 

integrating the acceleration data. 
5

Fig. 4 Acceleration and velocity from the original (red) and baseline 

shifted (black) data

2.1.2 Step 2 – Locate the Peak

Following integration of the acceleration record, the peak velocity within a time frame of interest 

is identified. However, this point does not always represent the end to the initial rise in velocity;

for example, it could be a secondary peak that occurs much later in time than the initial velocity

rise, as shown in Fig. 5. Choosing the secondary peak as the peak velocity would enlarge the 

time-to-peak velocity and therefore suggest a milder loading on the occupant than what actually 

occurred. This is resolved by first finding all local maxima in the velocity record that have a 

magnitude greater than 90% of the absolute peak. The local maximum just prior to the absolute 

peak is then selected as the new peak velocity. This search is repeated with the new peak velocity 

from the previous iteration until no local maxima exist that meet the 90% threshold. It should be 

noted that 90% was generally found to be the largest threshold that yielded the same local 

maximum as analysts chose for a majority of the LFT&E cases examined during the construction 

of this method.
6

Fig. 5 The absolute (red) and final (blue) peak velocities

2.1.3 Step 3 – Calculate Velocity Slope

Once the final peak velocity has been identified, an assumption of constant acceleration is used 

to define a velocity slope. Three locations on the velocity trace between the start of the time 

frame of interest and the peak velocity must be found. They are the first data points that have 

velocity magnitudes exceeding 5%, 20%, and 95% of the final peak velocity. The first and last 

points are the start and end points, respectively, of the velocity slope. If the velocity record 

exhibits a monotonic rise between the 5% and 20% points (no negative derivatives are present), 

it is appropriate to set the start of the velocity slope relative to the difference between the final 

peak velocity and zero as shown in Fig. 6. If there is at least one negative derivative in the 5% to 

20% time window of the velocity record, the starting point of the slope must be recalculated. 
7

Fig. 6 Velocity slope from 5% (blue) to 95% (red) of the final peak 

velocity

To recalculate the starting point of the velocity slope, the data point immediately following the 

last negative derivative in the window is identified and used to replace zero as the baseline for 

the 5% calculation. In other words, the velocity slope now travels from 5% of the difference 

between the final peak velocity and the point after the last negative derivative to 95% of the 

difference between the final peak velocity and zero (as shown in Fig. 7).
8

Fig. 7 Velocity slope from 5% (blue) of the difference between the 

final peak velocity and the point after the last negative 

derivative (green) to 95% (red) of the difference between the 

final peak velocity and zero

2.1.4 Step 4 – Calculate Time-to-Peak

Finding the start and end times of the velocity approximation is accomplished by extending the 

slope line (Fig. 8). The start time is the intercept between the slope line and zero velocity, and 

the end time is the intercept between the slope line and peak velocity. Time-to-peak is simply the 

difference between the end and start times. 
9

Fig. 8 The full approximation of the rise in velocity formed by 

extending (blue) the velocity slope (red) developed in Step 3

3. Conclusion

The simple method explained in this report was developed to be applicable to a large number of 

structural-velocity traces produced during LFT&E with a broad range of characteristics. It 

approximates the velocity of a structural component from the constituent acceleration record in 

order to determine peak velocity and the time taken to achieve peak velocity. Together, these 

metrics are useful when assessing the response of a vehicle exposed to an underbody-blast event 

and, consequently, characterizing the environment of mounted vehicle occupants. 
10

4. References

1. MIL-STD-810G. Environmental engineering considerations and laboratory tests.

US Army Test and Evaluation Command: US Department of Defense; 2008 Oct 31. 

2. Yoganandan N, Pintar F, Butler J, Reinartz J, Sances A, Larson SJ. Dynamic response of 

human cervical spine ligaments. Spine. 1989;14(10):1102–1110.

3. Nordin M, Frankel VH. Basic biomechanics of the musculoskeletal system, 3rd ed. New 

York (NY): Lippincott Williams and Wilkins; 2001.

4. Gaberson HA. Pseudo velocity shock spectrum analysis data editing. Paper presented at: 

IMAC-XXVII. Proceedings of the SEM Conference & Exposition on Structural Dynamics; 

2009 Feb 9–12; Orlando (FL).
11

Appendix. MATLAB Script for Calculating Peak and Time-to-Peak Velocities

This appendix appears in its original form, without editorial change.
12

%Velocity and Time-to-peak Script

%Robert Spink, 26 June 2014

%Input variables are as follows:

%time - vector of time values

%vel - vector of velocity values

%search_start - start time for the data region of interest

%ssearch_stop - stop time for the data region of interest

%FIND START INDEX, STOP INDEX, START THRESHOLD, MIDDLE THRESHOLD, AND STOP THRESHOLD

start_index=find(time>search_start,1);

stop_index=find(time>search_stop,1)-1;

start_threshold=.05;

mid_threshold=.2;

stop_threshold=.95;

peak_compare=.90;

%FIND ALL LOCAL PEAKS

derivative=diff(vel(start_index:stop_index));

peak_vector=zeros(stop_index-start_index,1);

for k=2:length(peak_vector);

if ((derivative(k-1)<0&derivative(k)>=0)&vel(k)<0)|((derivative(k-1)... 

>0&derivative(k)<=0)&vel(k)>0);

peak_vector(k)=vel(k+start_index-1);

end

end

%PROCESS DATA

[vel_100,vel_100_index]=max(vel(start_index:stop_index));

vel_100_index=vel_100_index+start_index-1;

recursive_peak=length(find(peak_vector(1:vel_100_index-start_index+1-1)>peak_compare*vel_100));

while recursive_peak>0;

vel_100_index=find(peak_vector(1:vel_100_index-start_index+1-1)... 

>peak_compare*vel_100,1,'last')+start_index-1;

vel_100=vel(vel_100_index);

recursive_peak=length(find(peak_vector(1:vel_100_index-start_index+1-1)... 

>peak_compare*vel_100));

end

time_100=time(vel_100_index);

vel_95_index=find(vel(start_index:vel_100_index-1)<vel_100*stop_threshold,1,'last')+start_index;

vel_95=vel(vel_95_index);

time_95=time(vel_95_index);

vel_20_index=find(vel(start_index:vel_95_index-1)<vel_100*mid_threshold,1,'last')+start_index;

vel_20=vel(vel_20_index);

time_20=time(vel_20_index);

vel_5_index=find(vel(start_index:vel_20_index-1)<vel_100*start_threshold,1,'last')+start_index;

vel_5=vel(vel_5_index);

time_5=time(vel_5_index);

if size(find(derivative(vel_5_index-start_index+1:vel_20_index-start_index+1)<0))>0;

last_inflection_index=find(derivative(vel_5_index-start_index+1:vel_20_index...

-start_index+1)<0,1,'last')+vel_5_index;

last_inflection_vel=vel(last_inflection_index);

vel_5_index=find(vel(start_index:vel_100_index)<(last_inflection_vel+(start_threshold*... 

(vel_100-last_inflection_vel))),1,'last')+start_index;

vel_5=vel(vel_5_index);

time_5=time(vel_5_index);

end

slope=(vel_95-vel_5)/(time_95-time_5);

peak_time=((vel_100-vel_95)/slope)+time_95;

start_time=time_95-((vel_95-0)/slope);

t2p=peak_time-start_time;
13

List of Symbols, Abbreviations, and Acronyms

AA anti-alias

dB decibel

g acceleration due to earth’s gravity

Hz hertz

kHz kilohertz

LFT&E Live Fire Test and Evaluation

m/s2 meter per second squared
14

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