3. Signal preprocessing for crash pulses

Raw accelerometer channels from a crash test are never ready for injury criteria calculation the moment they leave the data acquisition system. Even a perfectly mounted sensor records a small DC offset, a slow thermal drift, and a residual offset introduced by the amplifier and the analog-to-digital converter. If these artifacts are left in place, a single integration to velocity and a second integration to displacement will accumulate them into a large, physically meaningless ramp. The purpose of preprocessing is to remove these non-physical components while preserving the genuine crash pulse, and to establish a defensible time-zero and amplitude-zero reference so that every downstream channel — acceleration, velocity, displacement, and injury criteria — shares the same coordinate and sign convention.

Reference conventions used throughout this chapter

Before any operation, fix the conventions. In this course, the vehicle longitudinal axis is positive in the forward direction of travel; a frontal impact therefore produces a predominantly negative longitudinal acceleration on a body-mounted sensor. Time zero (t = 0) is defined as the first sample at which the filtered longitudinal acceleration exceeds the trigger threshold, typically 0.5 g to 1.0 g sustained for at least 3 ms. All samples before t = 0 constitute the pre-trigger window, and this window is the statistical basis for baseline estimation. Every figure and equation below follows this convention; if a lab uses the opposite sign for the longitudinal axis, the sign of the pulse flips but the preprocessing logic is unchanged.

Why detrending and baseline correction are separate operations

Detrending removes a slow, systematic variation across the record — most commonly a linear drift caused by thermal effects in the sensor or by a slight tilt of the mounting block relative to the gravity vector. Baseline correction removes a constant offset, the mean value of the signal in a quiescent region. They are related but not interchangeable: a linear detrend applied over the whole record will also remove part of the genuine pulse if the pulse is asymmetric, while a pure mean subtraction cannot remove drift. In practice, the correct order is: estimate the baseline from the pre-trigger window, subtract it, then evaluate whether residual drift remains and, if so, apply a linear detrend fitted only to the pre-trigger and post-crash quiescent regions — never across the pulse itself.

Estimating the baseline from pre-trigger data

The pre-trigger window should be long enough to average out noise but short enough to avoid drift accumulation. A practical rule is to use between 50 ms and 200 ms of pre-trigger data, ending at least 5 ms before t = 0 to exclude the rising edge of the trigger. For a channel sampled at 10 kHz, a 100 ms window contains 1000 samples — ample for a stable mean. The baseline estimate is simply the arithmetic mean of that window:

b = (1/N) * sum(x[n]) for n in pre-trigger window
x_corrected[n] = x_raw[n] - b

For a linear detrend, fit x[n] ≈ a + b·n by least squares over the pre-trigger window (and, if available, a post-event quiescent window), then subtract the fitted line from the entire record. The slope b is the drift rate in g per sample; converting it to g/s makes it comparable across sampling rates. A drift rate above roughly 0.05 g/s in a piezoelectric channel usually indicates a charge amplifier issue or a mounting problem and should be flagged rather than silently corrected.

Zeroing and the trigger reference

Zeroing is the final step that ties the corrected signal to the trigger definition. After baseline subtraction, the value at t = 0 should be close to the trigger threshold, not to zero — the pulse has already begun. What must be zero is the pre-trigger mean, and the time axis must be shifted so that t = 0 coincides with the defined trigger sample. If the acquisition system stores a trigger index, apply the shift by re-indexing; if not, locate the first sample satisfying the threshold-and-duration rule and subtract its index from all time stamps. This ensures that velocity obtained by integrating from t = 0 starts from a known zero initial condition, which is the assumption behind the standard crash pulse velocity change (delta-v) calculation.

Worked example: a frontal longitudinal channel

Consider an illustrative (not measured) longitudinal channel sampled at 10 kHz with a 100 ms pre-trigger window. Suppose the raw pre-trigger mean is +0.18 g and a least-squares fit over that window gives a slope of +0.012 g/s. Subtracting the mean and the fitted line yields a corrected pre-trigger mean of 0.00 g and a residual slope below 0.001 g/s. The trigger is then located at the first sample where the corrected signal exceeds -0.5 g for 3 ms; the time axis is shifted so that sample becomes t = 0. Integrating the corrected acceleration from t = 0 to the end of the pulse gives a delta-v whose final value should return to a plateau once the vehicle has stopped — a flat post-impact velocity trace is the primary verification that baseline and zeroing were done correctly.

Verification and common failure modes

Three checks confirm that preprocessing is complete and defensible. First, the corrected pre-trigger mean must be within ±0.02 g of zero and the residual slope below 0.001 g/s. Second, the integrated velocity must reach a stable plateau after the pulse; a continuing upward or downward ramp indicates residual offset or drift. Third, the displacement obtained by a second integration should return to a physically plausible final value — a large residual displacement usually means a small baseline error was integrated twice. Typical failure symptoms and their causes: a velocity trace that never flattens points to an uncorrected DC offset; a velocity trace that curves smoothly through the whole record points to uncorrected drift; a delta-v that is systematically low points to a baseline estimated from post-trigger samples. Each of these is corrected by revisiting the pre-trigger window definition and the order of operations, not by post-hoc scaling of the result.

Preprocessing checklist

Once these steps are complete, the channel is ready for filtering and injury-criterion calculation. The key discipline is that baseline estimation, detrending, and zeroing are all anchored to the pre-trigger window and to a single, documented trigger definition — not to the pulse itself. Keeping that anchor consistent across every channel is what makes the resulting delta-v, displacement, and injury values comparable between tests and between laboratories.