Tutorial Acceleration Noise

 Acceleration Noise is the standard deviation of the acceleration of a specific link. Acceleration noise is calculated from the Time Step Data output file to match the Acceleration Noise in given in the Link Performance Measures output file. To verify acceleration noise from the Time Step Data file, first filter out any vehicles that are present during the warm up time. Then filter out an vehicles that do not fully travel the link during simulation time. This includes vehicles that are present on the link at the start of the simulation or are present on the link at the end of the simulation. Once the vehicles for the link are appropriately filtered, then proceed to the calculation of the standard deviation.The standard deviation can be calculated from the Time Step Data file with the following equation: $$σ=\left\{ \left(\frac{1}{T}\right)\int_{1}^N\ [a(t)]^{2}dt\right\}^{1/2}$$ Assuming mean (μ)=0 (6.1) $$σ=\left\{ \left(\frac{1}{T}\right)\int_{1}^N\ [a(t)-μ]^{2}dt\right\}^{1/2}$$ Assuming for mean (μ) to be $$\neq0$$ (6.2) Where: To calculate $$T$$ use the following equation for each vehicle: $$ T =\sum_{i=1}^\N\ dt$$, where $$ dt $$ is the time step used in the SwashSim simulation and $$N$$ being the total number of time steps spent of the link. To calculate $$μ$$ use the following equation: $$μ =\frac{1}{T} \displaystyle\sum_{i=1}^{N} a(t)$$