Derivative

Overview

This test metric calculates the rate of change of the signal's input (x-values) with respect to the signal's output (y-values).

Required Inputs

• Time History Signal

Calculation

1. Time is converted into seconds to ensure consistency across signal
2. Central difference method is applied to calculate derivative
   • First order central difference forumula is applied at the start and end point of signal
   • Second order central difference formula is applied to the interior points

$$First\,Order\,Central\,Difference (\frac{d}{dt}f(t) )= \frac{f(t+\Delta t)-f(\Delta t)}{\Delta t}$$ $$Second\,Order\,Central\,Difference (\frac{d}{dt}f(t) )= \frac{f(t+\Delta t)-f(t-\Delta t)}{2\Delta t}$$

Derivative Example

Before derivative is applied to signal

After derivative is applied to signal