Baseline Correction

Baseline correction can be applied to correct the acceleration record to avoid displacement shift.

When acceleration is applied as input via SPCD, the integration of displacement results may diverge at the last point of simulation. Baseline correction can be used to correct the acceleration input. The BASELIN Subcase and BASELIN Bulk Data Entry pair can be used to apply baseline correction.

There are two methods by which Baseline correction can be applied. For both cases, the acceleration load is corrected by fitting the load to a polynomial with coefficients $C_{0}$ $C_{0}$ , $C_{1}$ $C_{1}$ , and $C_{2}$ $C_{2}$ .

Acceleration Method (METHOD=ACCE on BASELIN Bulk Data)

The baseline correction to the acceleration load is calculated as:

a_{b} (t) = C_{0} + C_{1} t + C_{2} t^{2}

$a_{b} (t) = C_{0} + C_{1} t + C_{2} t^{2}$

The corrected acceleration load is:

a_{c} (t) = a (t) - a_{b} (t)

$a_{c} (t) = a (t) - a_{b} (t)$

The coefficients of the polynomial are evaluated by minimizing the square of the corrected acceleration load.

S (C_{1}, C_{2}, C_{3}) = min [n \sum i = 1 {(a_{c} (t_{i}))}^{2}]

$S (C_{1}, C_{2}, C_{3}) = \min [\sum_{i = 1}^{n} {(a_{c} (t_{i}))}^{2}]$

Where,

$C_{0}$ $C_{0}$ , $C_{1}$ $C_{1}$ , and $C_{2}$ $C_{2}$: Coefficients of the polynomial, which are unknowns to be calculated from the above minimization functions.
$S$ $S$: Function of polynomial coefficients.
$a (t)$ $a (t)$: Input acceleration load.
$a_{b} (t)$ $a_{b} (t)$: Baseline correction of the acceleration.
$a_{c} (t)$ $a_{c} (t)$: Corrected acceleration after baseline correction.
$t$ $t$: Time associated with each acceleration data point in the record.
$n$ $n$: Total number of acceleration data points in the record (points on TABLED# entry referenced on TLOAD1 entry).

Velocity Method (METHOD=VELO on BASELIN Bulk Data)

The baseline correction to the acceleration load is calculated as:

a_{b} (t) = C_{0} + C_{1} (\frac{t - T_{1}}{T_{2} - T_{1}}) + C_{2} {(\frac{t - T_{1}}{T_{2} - T_{1}})}^{2}

$a_{b} (t) = C_{0} + C_{1} (\frac{t - T_{1}}{T_{2} - T_{1}}) + C_{2} {(\frac{t - T_{1}}{T_{2} - T_{1}})}^{2}$

The corrected acceleration load is:

a_{c} (t) = a (t) - a_{b} (t)

$a_{c} (t) = a (t) - a_{b} (t)$

The corrected velocity is:

v_{c} (t) = v (T_{1}) + T_{2} \int T_{1} a_{c} (t) d t

$v_{c} (t) = v (T_{1}) + \int_{T_{1}}^{T_{2}} a_{c} (t) d t$

The coefficients of the polynomial are evaluated by minimizing the integration of square of the corrected velocity load.

S (C_{1}, C_{2}, C_{3}) = min ⎡ ⎢ ⎣ T_{2} \int T_{1} {(v_{c} (t))}^{2} d t ⎤ ⎥ ⎦

$S (C_{1}, C_{2}, C_{3}) = \min [\int_{T_{1}}^{T_{2}} {(v_{c} (t))}^{2} d t]$

Where,

$C_{0}$ $C_{0}$ , $C_{1}$ $C_{1}$ , and $C_{2}$ $C_{2}$: Coefficients of the polynomial, which are unknowns to be calculated from the above minimization functions.
$S$ $S$: Function of polynomial coefficients.
$a_{b} (t)$ $a_{b} (t)$: Baseline correction of the acceleration.
$a_{c} (t)$ $a_{c} (t)$: Corrected acceleration after baseline correction.
$v (t)$ $v (t)$: Velocity load.
$v_{c} (t)$ $v_{c} (t)$: Corrected velocity after baseline correction.
$t$ $t$: Time associated with each acceleration data point in the record.
$T_{1}$ $T_{1}$ and $T_{2}$ $T_{2}$: Initial and final total time.; For both continuation subcases or independent subcases, the baseline correction calculation is conducted for each subcase, and separate $C_{0}$ $C_{0}$ , $C_{1}$ $C_{1}$ , and $C_{2}$ $C_{2}$ coefficients are calculated for each subcase for baseline correction. In the case of continuation subcases, the values of $T_{1}$ $T_{1}$ and $T_{2}$ $T_{2}$ used in the calculation are still the total time.