COSIN/io 2D Road Type: stochastic_uneven

In the first step, discrete white noise signals are formed on the basis of nearly uniformly distributed random numbers; two of these assigned to every 10mm of travel path. The distribution of these random numbers is approximated by summing up several equally distributed random numbers, taking advantage of the law of large numbers of mathematical statistics.

Next, these values are integrated with respect to travel distance, using a simple first order time-discrete integration filter. The reason for not using a pure integrator is to cut off extremely low frequencies, which would result in large road elevation values, not at all affecting vehicle dynamics.

The independent variable of the filter is not time, but travel path. This is why the filter cut-off frequency is controlled by a path constant instead of a time constant. Approximate power spectral density (PSD) of the road surface profile is given by:

Where,

The filter process results in two realizations of the approximate white velocity noise; two signals, the derivatives of which are close to white noise. Signals with this property are known as road profiles with waviness w = 2 (Refer to ISO 8608). Several investigations show the waviness derived from measured road displacement PSDs ranges from about 1.8 to 2.2.

The reference spectral density value , with , is used in ISO 8608 to classify road surface profiles, according to the following table:

Road class	min. value	mean value	max. value
A	-	1	2
B	2	4	8
C	8	16	32
D	32	64	128
E	128	256	512
F	512	1024	2048
G	2048	4096	8192
H	8192	16384	-

The last step in the generation of the stochastic uneven road profiles is to linearly combine the two realizations , of the above mentioned process, resulting in the left and right profile , . This is done such that these two signals are completely independent, if correlation_rl = 0.0, and identical, if correlation_rl = 1.0:

For the data supply, COSIN/road searches for the data block $stochastic_uneven, and reads:

Name of Variable		Unit	Meaning
One of	reference_spectral_density	m3
	ISO_8608_road_class	A, B, ..	ISO 8608 road class, according to table above. Mean value of the respective class is used.
path_constant		m	Path constant S to control high-pass integration filter cut-off frequency in path domain. Parameter is optional, default value is 1000 m.
correlation_rl		-	Variable to control correlation between left and right track: no correlation, if zero; complete correlation (left track = right track), if one. Any value between 0 and 1 is allowed.